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Over the last two decades, the competing orders in high-$T_{c}$ cuprates have been intensely studied, such as pseudogap phase, charge density waves (CDW), and pair density waves (PDW), which are thought to play a crucial role in high-temperature superconductivity. Using the $t$-$J$ model on a square lattice as the simplest model for high-$T_{c}$ cuprates, we employed the fermionic tensor product state (fTPS) method for numerical investigations. Our study revealed new types of PDW states alongside the well-known $d$-wave state and the recently discovered fluctuating PDW state within the low-energy subspace of the $t$-$J$ model. We believe that the competition among these states in the underdoped region suggests the potential existence of a fluctuating quantum liquid of PDW states, providing direct evidence for the pseudogap phase's "cheap vortex" scenario. Furthermore, we discuss the potential experimental implication of our discovery., Comment: 10 pages, 17 figures

Two-dimensional (2D) superconductors that reside on substrates must be influenced by Rashba spin-orbit coupling (SOC). The intriguing effect of Rashba-type SOCs on iron-based superconductors (IBSs) has remained largely a mystery. In this work, we unveil modified Landau-level spectroscopy and the intricate band splitting of FeSe monolayers through the precision of scanning tunneling spectroscopy, which unequivocally demonstrates the presence of Rashba SOC. The discovery sheds light on a nonparabolic electron band at the X/Y point, displaying a distinctive Landau quantization behavior characterized by $E_n\propto(nB)^{4/3}$. The theoretical model aligns with our experimental insights, positing that the k$^4$-term of the electron band becomes predominant and profoundly reshapes the band structure. Our research underscores the pivotal role of the Rashba SOC effect on 2D superconductors and sets the stage to probe new quantum states in systems with remarkably low carrier concentrations., Comment: 21 pages, 5 figures

The interplay between symmetry and topological properties plays a very important role in modern physics. In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been systematically studied for bosonic systems. Very recently, the concept of SET phases has been generalized into fermionic systems and their corresponding classification schemes are also proposed. Nevertheless, how to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem. In this paper, we first construct exactly solvable models for non-anomalous non-chiral 2+1D fSET phases, namely, the symmetry-enriched fermionic string-net models, which are described by commuting-projector Hamiltonians whose ground states are the fixed-point wavefunctions of each fSET phase. Mathematically, we provide a partial definition to $G$-graded super fusion category, which is the input data of a symmetry-enriched fermionic string-net model. Next, we construct exactly solvable models for non-chiral 2+1D fSET phases with 't Hooft anomaly, especially the $H^3(G,\mathbb{Z}_2)$ fermionic 't Hooft anomaly which is different from the well known bosonic $H^4(G,U(1)_T)$ anomaly. In our construction, this $H^3(G,\mathbb{Z}_2)$ fermionic 't Hooft anomaly is characterized by a violation of fermion-parity conservation in some of the surface $\mathcal{F}$-moves (a kind of renormalization moves for the ground state wavefunctions of surface SET phases), and also by a new fermionic obstruction $\Theta$ in the surface pentagon equation. We demonstrate this construction in a concrete example that the surface topological order is a $\mathbb{Z}_4$ gauge theory embedded into a fermion system and the total symmetry $G^f=\mathbb{Z}_2^f\times\mathbb{Z}_2\times\mathbb{Z}_4$., Comment: 41 pages

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

In the milli-Hertz frequency band, stochastic gravitational-wave background can be composed of both astronomical and cosmological sources, both can be anisotropic. Numerically depicting these anisotropies can be critical in revealing the underlying properties of their origins. For the first time, we perform a theoretical analysis of the constraining ability of TianQin on multiple moments of the stochastic background. First, we find that with a one-year operation, for a background with a signal-to-noise ratio of 16, TianQin can recover the multiple moments up to $l=4$. We also identified a unique feature of the stochastic background sky map, which is the mirror symmetry along the fixed orbital plane of TianQin. Thirdly, we explain the difference in anisotropy recovering ability between TianQin and LISA, by employing the criteria of the singularity of the covariance matrix (which is the condition number). Finally, we find that since the different data channel combinations correspond to different singularities, certain combinations might have an advantage in stochastic background map-making. We believe that the findings of this work can provide an important reference to future stochastic background analysis pipelines. It can also serve as a guideline for designing better gravitational-wave detectors aiming to decipher anisotropies in the stochastic background., Comment: 12 pages, 6 figures

Space-borne detectors, including TianQin and Laser Interferometry Space Antenna (LISA), are tasked with the simultaneous observation of Galactic foreground, astrophysical and cosmological stochastic gravitational-wave backgrounds (SGWBs). For the first time, we employ a space-borne detector network to identify the multi-component SGWB. Specifically, we develop a tailored likelihood for cross-correlation detection with such networks. Combined with the likelihood, we use the simulated datasets of the TianQin + LISA network to conduct model selection and parameter estimation. Our results indicate that, after 4 years of operation, the network could detect a single SGWB from either astrophysical or cosmological origins, with an energy density $\Omega_{\rm ast/cos}$ (10 mHz) on the order of $10^{-12}$, despite the presence of a Galactic foreground. Furthermore, to distinguish the cosmological background from both a Galactic foreground and the expected astrophysical background, the energy density $\Omega_{\rm cos}$ should reach around $2\times 10^{-11}$., Comment: 17 pages, 9 figures

We give a simple proof about the topological rigidity of closures of certain sparse unipotent orbits in $G/\Gamma$ where $G=\prod_{i=1}^k\operatorname{SL}_2(\mathbb R)$ and $\Gamma$ is an irreducible lattice in $G$., Comment: 18 pages

While diffusion models have shown impressive performance in 2D image/video generation, diffusion-based Text-to-Multi-view-Video (T2MVid) generation remains underexplored. The new challenges posed by T2MVid generation lie in the lack of massive captioned multi-view videos and the complexity of modeling such multi-dimensional distribution. To this end, we propose a novel diffusion-based pipeline that generates high-quality multi-view videos centered around a dynamic 3D object from text. Specifically, we factor the T2MVid problem into viewpoint-space and time components. Such factorization allows us to combine and reuse layers of advanced pre-trained multi-view image and 2D video diffusion models to ensure multi-view consistency as well as temporal coherence for the generated multi-view videos, largely reducing the training cost. We further introduce alignment modules to align the latent spaces of layers from the pre-trained multi-view and the 2D video diffusion models, addressing the reused layers' incompatibility that arises from the domain gap between 2D and multi-view data. In support of this and future research, we further contribute a captioned multi-view video dataset. Experimental results demonstrate that our method generates high-quality multi-view videos, exhibiting vivid motions, temporal coherence, and multi-view consistency, given a variety of text prompts., Comment: Our project page is at https://hi-zhengcheng.github.io/vividzoo/

The physical nature of pseudogap phase is one of the most important and intriguing problems towards understanding the key mechanism of high temperature superconductivity in cuprates. Theoretically, the square-lattice $t$-$J$ model is widely believed to be the simplest toy model that captures the essential physics of cuprate superconductors. We employ the Grassmann tensor product state approach to investigate uniform states in the underdoped ($\delta \lesssim 0.1$) region. In addition to the previously known uniform $d$-wave state, we discover a strongly fluctuating pair density wave (PDW) state with wave vector $Q = (\pi, \pi)$. This fluctuating PDW state weakly breaks the $C_4$ rotational symmetry of the square lattice and has a lower or comparable energy to the $d$-wave state (depending on doping and the $t/J$ ratio), making it a promising candidate state for describing the pseudogap phase., Comment: 10 pages, 13 figures, references added

It has long been believed that doped quantum spin liquids (QSLs) can give rise to fascinating quantum phases, including the possibility of high-temperature superconductivity (SC) as proposed by P. W. Anderson's resonating valence bond (RVB) scenario. The Kagome lattice $t$-$J$ model is known to exhibit spin liquid behavior at half-filling, making it an ideal system for studying the properties of doped QSL. In this study, we employ the fermionic projected entangled simplex state (PESS) method to investigate the ground state properties of the Kagome lattice $t$-$J$ model with $t/J = 3.0$. Our results reveal a phase transition from charge density wave (CDW) states to uniform states around a critical doping level $\delta_c \approx 0.27$. Within the CDW phase, we observe different types of Wigner crystal (WC) formulated by doped holes that are energetically favored. As we enter the uniform phase, a non-Fermi liquid (NFL) state emerges within the doping range $0.27 < \delta < 0.32$, characterized by an exponential decay of all correlation functions. With further hole doping, we discover the appearance of a pair density wave (PDW) state within a narrow doping region $0.32 < \delta < 1/3$. We also discuss the potential experimental implications of our findings., Comment: 11 pages, 17 figures

Weak-signal limit is often used in estimating stochastic gravitational-wave background (SGWB) intensities. This approximation fails and the signal-to-noise ratio (SNR) can be much weaker when background signals are loud compared to the detector noise. In this work, we highlight this limitation for the SGWB detection using space-borne detector networks. For the TianQin + LISA network, the SNR estimated under the weak-signal limit might be off by as large as an order of magnitude. Contour plots of SNR over the parameter spaces are also presented to indicate regions susceptible to this discrepancy. Our results suggest that DA and DB type extragalactic double white dwarfs may yield an SGWB with SNR surpassing 100 after 1 year of operation in the weak-signal-limit scenario, with a redshift-independent merger rate of about $500\,\,{\rm Mpc^{-3}\,Myr^{-1}}$. In fact, this value falls significantly below the necessary threshold. Similar influences arise for first-order phase transitions, yet pinning down parameter regions remains formidable due to model uncertainties., Comment: 11 pages, 7 figures

The topological aspects of Einstein gravity suggest that topological invariance could be a more profound principle in understanding quantum gravity. In this work, we explore a topological supergravity action that initially describes a universe without Riemann curvature, which seems trivial. However, we made a surprising discovery by introducing a small deformation parameter $\lambda$, which can be regarded as an AdS generalization of supersymmetry (SUSY). We find that the deformed topological quantum field theory (TQFT) becomes unstable at low energy, resulting in the emergence of a classical metric, whose dynamics are controlled by the Einstein equation. Our findings suggest that a quantum theory of gravity could be governed by a UV fixed point of a SUSY TQFT, and classical spacetime ceases to exist beyond the Planck scale., Comment: 12 pages, no figure

In this note, we initiate a study on Jarn\'ik-Besicovitch type theorems for semisimple algebraic groups from the representation-theoretic point of view. Let $\rho:\mathbf G\to\operatorname{\mathbf{GL}}(V)$ be an irreducible $\mathbb Q$-rational representation of a connected semisimple $\mathbb Q$-algebraic group $\mathbf G$ on a complex vector space $V$ and $\{a_t\}_{t\in\mathbb R}$ a one-parameter subgroup in a $\mathbb Q$-split torus in $\mathbf G$. We define a subset $S_\tau(\rho,\{a_t\}_{t\in\mathbb R})$ of Diophantine elements of type $\tau$ in $\mathbf G(\mathbb R)$ in terms of the representation $\rho$ and the subgroup $\{a_t\}_{t\in\mathbb R}$, and prove formulas for the Hausdorff dimension of the complement of $S_{\tau}(\rho,\{a_t\}_{t\in\mathbb R})$. As corollaries, we deduce several Jarn\'ik-Besicovitch type theorems.

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the "boundary-changing operators" on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee and Tri-critical Ising models to compute the scaling dimensions explicitly based on the corresponding FP tensor. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door towards understanding CFT in higher dimensions., Comment: 16 pages, 17 figures, 12 tables; Added numerical test for Yang-Lee and Tri-critical Ising model

In the past decade, there has been a systematic investigation of symmetry-protected topological (SPT) phases in interacting fermion systems. Specifically, by utilizing the concept of equivalence classes of finite-depth fermionic symmetric local unitary (FSLU) transformations and the fluctuating decorated symmetry domain wall picture, a large class of fixed-point wave functions have been constructed for fermionic SPT (FSPT) phases. Remarkably, this construction coincides with the Atiyah-Hirzebruch spectral sequence, enabling a complete classification of FSPT phases. However, unlike bosonic SPT phases, the stacking group structure in fermion systems proves to be much more intricate. The construction of fixed-point wave functions does not explicitly provide this information. In this paper, we employ FSLU transformations to investigate the stacking group structure of FSPT phases. Specifically, we demonstrate how to compute stacking FSPT data from the input FSPT data in each layer, considering both unitary and anti-unitary symmetry, up to 2+1 dimensions. As concrete examples, we explicitly compute the stacking group structure for crystalline FSPT phases in all 17 wallpaper groups and the mixture of wallpaper groups with onsite time-reversal symmetry using the fermionic crystalline equivalence principle. Importantly, our approach can be readily extended to higher dimensions, offering a versatile method for exploring the stacking group structure of FSPT phases., Comment: Correct some errors in 1+1D case. Add more examples for 2+1D crystalline FSPT protected by symmetries being the mixture of wallpaper groups with onsite time-reversal symmetry

The rapidly expanding field of metabolomics presents an invaluable resource for understanding the associations between metabolites and various diseases. However, the high dimensionality, presence of missing values, and measurement errors associated with metabolomics data can present challenges in developing reliable and reproducible methodologies for disease association studies. Therefore, there is a compelling need to develop robust statistical methods that can navigate these complexities to achieve reliable and reproducible disease association studies. In this paper, we focus on developing such a methodology with an emphasis on controlling the False Discovery Rate during the screening of mutual metabolomic signals for multiple disease outcomes. We illustrate the versatility and performance of this procedure in a variety of scenarios, dealing with missing data and measurement errors. As a specific application of this novel methodology, we target two of the most prevalent cancers among US women: breast cancer and colorectal cancer. By applying our method to the Wome's Health Initiative data, we successfully identify metabolites that are associated with either or both of these cancers, demonstrating the practical utility and potential of our method in identifying consistent risk factors and understanding shared mechanisms between diseases.

We introduce neural lithography to address the 'design-to-manufacturing' gap in computational optics. Computational optics with large design degrees of freedom enable advanced functionalities and performance beyond traditional optics. However, the existing design approaches often overlook the numerical modeling of the manufacturing process, which can result in significant performance deviation between the design and the fabricated optics. To bridge this gap, we, for the first time, propose a fully differentiable design framework that integrates a pre-trained photolithography simulator into the model-based optical design loop. Leveraging a blend of physics-informed modeling and data-driven training using experimentally collected datasets, our photolithography simulator serves as a regularizer on fabrication feasibility during design, compensating for structure discrepancies introduced in the lithography process. We demonstrate the effectiveness of our approach through two typical tasks in computational optics, where we design and fabricate a holographic optical element (HOE) and a multi-level diffractive lens (MDL) using a two-photon lithography system, showcasing improved optical performance on the task-specific metrics., Comment: The paper, titled "Close the Design-to-Manufacturing Gap in Computational Optics with a 'Real2Sim' Learned Two-Photon Neural Lithography Simulator," has been accepted for presentation at SIGGRAPH Asia 2023. This version offers a more comprehensive and accessible read. Project page: https://neural-litho.github.io

Space-based gravitational wave detectors such as TianQin, LISA, and TaiJi have the potential to outperform themselves through joint observation. To achieve this, it is desirable to practice joint data analysis in advance on simulated data that encodes the intrinsic correlation among the signals found in different detectors that operate simultaneously. In this paper, we introduce \texttt{GWSpace}, a package that can simulate the joint detection data from TianQin, LISA, and TaiJi. The software is not a groundbreaking work that starts from scratch. Rather, we use as many open-source resources as possible, tailoring them to the needs of simulating the multi-mission science data and putting everything into a ready-to-go and easy-to-use package. We shall describe the main components, the construction, and a few examples of application of the package. A common coordinate system, namely the Solar System Barycenter (SSB) coordinate system, is utilized to calculate spacecraft orbits for all three missions. The paper also provides a brief derivation of the detection process and outlines the general waveform of sources detectable by these detectors., Comment: 24 pages, 13 figures, GWSpace will be uploaded at https://github.com/TianQinSYSU/GWSpace

We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS., Comment: 13 pages; 19 figures

Motivated by the novel phenomena observed in the layered material $\rm SrCu_2(BO_3)_2$, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for $\rm SrCu_2(BO_3)_2$. However, the nature of its quantum phase transition from the plaquette valence-bond solid (PVBS) to antiferromagnetic (AFM) phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to $20 \times 20$ sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the PVBS and AFM phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of $\rm SrCu_2(BO_3)_2$., Comment: 5+6 pages; 4+5 figures; 3 tables

Manually reading and logging gauge data is time inefficient, and the effort increases according to the number of gauges available. We present a computer vision pipeline that automates the reading of analog gauges. We propose a two-stage CNN pipeline that identifies the key structural components of an analog gauge and outputs an angular reading. To facilitate the training of our approach, a synthetic dataset is generated thus obtaining a set of realistic analog gauges with their corresponding annotation. To validate our proposal, an additional real-world dataset was collected with 4.813 manually curated images. When compared against state-of-the-art methodologies, our method shows a significant improvement of 4.55 in the average error, which is a 52% relative improvement. The resources for this project will be made available at: https://github.com/fuankarion/automatic-gauge-reading.

TianQin and LISA are space-based laser interferometer gravitational wave (GW) detectors planned to be launched in the mid-2030s. Both detectors will detect low-frequency GWs around $10^{-2}\,{\rm Hz}$, however, TianQin is more sensitive to frequencies above this common sweet-spot while LISA is more sensitive to frequencies below $10^{-2}\,{\rm Hz}$. Therefore, TianQin and LISA will be able to detect the same sources but with different accuracy depending on the source and its parameters. We consider some of the most important astrophysical sources -- massive black hole binaries, stellar-mass black hole binaries, double white dwarfs, extreme mass ratio inspirals, light and heavy intermediate mass ratio inspirals, as well as the stochastic gravitational background of astrophysical origin -- that TianQin and LISA will be able to detect. For each of these sources, we analyze how far they can be detected (detection distance) and how well their parameters can be measured (detection accuracy) using a Fisher Matrix analysis. We compare the results obtained by the three detection scenarios (TianQin alone, LISA alone, and joint detection by LISA and TianQin) highlighting the gains from joint detection as well as the contribution of TianQin and LISA to a combined study of astrophysical sources. In particular, we consider the different orientations, lifetimes, and duty cycles of the two detectors to explore how they can give a more complete picture when working together., Comment: 49 pages, 63 figures

Single gravitational-wave detectors face inherent limitations in detecting the anisotropy of the stochastic background. In this work, we explore the sensitivity to anisotropic backgrounds with a network of space-borne detectors. We find that the separation between detectors plays an important role in determining the sensitivity. For the first time, we observe as large as three orders of magnitude enhancement in detection sensitivity for the multipoles with $l=5$ and 6, compared to coinciding detectors. Coordinating and optimizing the separation between two space-borne detectors can significantly enhance the network's sensitivity to the multipole components of the stochastic background. For the TianQin + LISA network, benefiting from detector separation, it is possible to achieve sensitivity levels of 2-3 orders of magnitude better than using TianQin or LISA detector alone. These findings pave the way to uncover the underlying physics of anisotropy through gravitational-wave detections., Comment: 19 pages, 13 figures

One challenge in exploratory association studies using observational data is that the signals are potentially weak and the features have complex correlation structures. False discovery rate (FDR) controlling procedures can provide important statistical guarantees for replicability in risk factor identification in exploratory research. In the recently established National COVID Collaborative Cohort (N3C), electronic health record (EHR) data on the same set of candidate features are independently collected in multiple different sites, offering opportunities to identify signals by combining information from different sources. This paper presents a general knockoff-based variable selection algorithm to identify mutual signals from unions of group-level conditional independence tests with exact FDR control guarantees under finite sample settings. This algorithm can work with general regression settings, allowing heterogeneity of both the predictors and the outcomes across multiple data sources. We demonstrate the performance of this method with extensive numerical studies and an application to the N3C data.

The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or $t$-$J$ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the $d+id$-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t$-$J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. Moreover, in the presence of anti-ferromagnetic order, a continuum effective field theory for holons is developed near half-filling. It reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. At a large value of $t/J$, the repulsive interaction dominates, leading to the non-Fermi liquid like behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Possible experimental detection of spin-charge separation phenomena is also discussed., Comment: 18 pages, 7 figures

We propose a minimal interacting lattice model for two-dimensional class-$D$ higher-order topological superconductors with no free-fermion counterpart. A Lieb-Schultz-Mattis-type constraint is proposed and applied to guide our lattice model construction. Our model exhibits a trivial product ground state in the weakly interacting regime, whereas, increasing electron interactions provoke a novel topological quantum phase transition to a $D_4$-symmetric higher-order topological superconducting state. The symmetry-protected Majorana corner modes are numerically confirmed with the matrix-product-state technique. Our theory paves the way for studying interacting higher-order topology with explicit lattice model constructions., Comment: 12 pages, 6 figures

The method of time delay interferometry (TDI) is proposed to cancel the laser noise in space-borne gravitational-wave detectors. Among all different TDI combinations, the most commonly used ones are the orthogonal channels A, E and T, where A and E are signal-sensitive and T is signal-insensitive. Meanwhile, for the detection of stochastic gravitational-wave background, one needs to introduce the overlap reduction function to characterize the correlation between channels. For the calculation of overlap reduction function, it is often convenient to work in the low-frequency approximation, and assuming the equal-arm Michelson channels. However, if one wishes to work on the overlap reduction function of $\rm A/E$ channels, then the low-frequency approximation fails. We derive the exact form of overlap reduction function for $\rm A/E$ channels. Based on the overlap reduction function, we calculate the sensitivity curves of TianQin, TianQin I+II and TianQin + LISA. We conclude that the detection sensitivity calculated with $\rm A/E$ channels is mostly consistent with that obtained from the equal-arm Michelson channels., Comment: 18 pages,10 figures

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbor couplings $J_{1x}$, $J_{1y}$ and the next nearest neighbor coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence bond solid phase is observed.(Of course, the possibility of weakly first order transition can not be fully excluded.) With growing $J_{1y}/J_{1x}$, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM--VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL--VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems., Comment: 5+7 pages, 4+11 figures

In this paper, we study the shrinking-target problem with target at infinity induced by the injectivity radius function under the action of a regular diagonalizable flow on $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$. In particular, we establish an explicit formula for the Hausdorff dimension of the subset of points $p$ whose orbit approaches the cusp infinitely often with a rate $\gamma\geq0$.

Limited throughput is a key challenge in in-vivo deep-tissue imaging using nonlinear optical microscopy. Point scanning multiphoton microscopy, the current gold standard, is slow especially compared to the wide-field imaging modalities used for optically cleared or thin specimens. We recently introduced 'De-scattering with Excitation Patterning or DEEP', as a widefield alternative to point-scanning geometries. Using patterned multiphoton excitation, DEEP encodes spatial information inside tissue before scattering. However, to de-scatter at typical depths, hundreds of such patterned excitations are needed. In this work, we present DEEP$^2$, a deep learning based model, that can de-scatter images from just tens of patterned excitations instead of hundreds. Consequently, we improve DEEP's throughput by almost an order of magnitude. We demonstrate our method in multiple numerical and physical experiments including in-vivo cortical vasculature imaging up to four scattering lengths deep, in alive mice.

The capture of compact objects by massive black holes in galaxies or dwarf galaxies will generate short gravitational wave signals, called extreme-mass-ratio bursts (EMRBs), before evolving into extreme-mass-ratio inspirals. Their detection will provide an investigation of the black hole properties and shed light on astronomy and astrophysics. In this work, we investigate the detection number of the TianQin observatory on EMRBs. Our result shows that TianQin can detect tens of EMRBs events during its mission lifetime. For those detected events, we use the Fisher information matrix to quantify these uncertainties in the inference of their parameters. We consider the possible network of TianQin+LISA and study how a network can improve parameter estimation. The result shows that, for most sources, the CO mass, the MBH mass, and the MBH spin can be determined with an accuracy of the order $10^{-1}$ and the sky localization can be determined with an accuracy of 10 square degrees. We further explore the gravitational wave background generated by those unsolved EMRBs and conclude that it is about $10^6$ times weaker than TianQin's sensitivity and thus it can be ignored.

We study the honeycomb lattice $t$-$J$ model using the fermionic tensor network approach. By examining the ansatz with various unit cells, we discover several different stripe states with different periods that compete strongly with uniform states. At very small doping $\delta < 0.05$, we find almost degenerate uniform $d$-wave superconducting ground states coexisting with antiferromagnetic order. While at larger doping $\delta > 0.05$, the ground state is an approximately half-filled stripe-ordered state, where the stripe period decreases with increasing hole doping $\delta$. Furthermore, the stripe states with the lowest variational energy always display $d_{x^2-y^2}$-wave pairing symmetry. The similarity between our results and those on the square lattice contributes to a more comprehensive understanding of doped Mott insulators., Comment: 14 pages, 19 figures

The detection of stochastic gravitational wave background (SGWB) is among the leading scientific goals of the space-borne gravitational wave observatory, which would have significant impact on astrophysics and fundamental physics. In this work, we developed a data analysis software, \texttt{TQSGWB}, which can extract isotropic SGWB using the Bayes analysis method based on the TianQin detector. We find that for the noise cross spectrum, there are imaginary components and they play an important role in breaking the degeneracy of the position noise in the common laser link. When the imaginary corrections are considered, the credible regions of the position noise parameters are reduced by two orders of magnitude. We demonstrate that the parameters of various signals and instrumental noise could be estimated directly in the absence of a Galactic confusion foreground through Markov chain Monte Carlo sampling. With only a three-month observation, we find that TianQin could be able to confidently detect SGWBs with energy density as low as $\Omega_{\rm PL} = 1.3 \times 10^{-12}$, $\Omega_{\rm Flat} = 6.0 \times 10^{-12}$, and $\Omega_{\rm SP} = 9.0 \times 10^{-12}$, for power-law, flat, and single-peak models respectively., Comment: 28 pages, 8 figures

For the analysis of a time-to-event endpoint in a single-arm or randomized clinical trial it is generally perceived that interpretation of a given estimate of the survival function, or the comparison between two groups, hinges on some quantification of the amount of follow-up. Typically, a median of some loosely defined quantity is reported. However, whatever median is reported, is typically not answering the question(s) trialists actually have in terms of follow-up quantification. In this paper, inspired by the estimand framework, we formulate a comprehensive list of relevant scientific questions that trialists have when reporting time-to-event data. We illustrate how these questions should be answered, and that reference to an unclearly defined follow-up quantity is not needed at all. In drug development, key decisions are made based on randomized controlled trials, and we therefore also discuss relevant scientific questions not only when looking at a time-to-event endpoint in one group, but also for comparisons. We find that different thinking about some of the relevant scientific questions around follow-up is required depending on whether a proportional hazards assumption can be made or other patterns of survival functions are anticipated, e.g. delayed separation, crossing survival functions, or the potential for cure. We conclude the paper with practical recommendations., Comment: 31 pages

The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically construct and classify all the crystalline topological superconductors and insulators in three-dimensional (3D) interacting fermion systems using the novel concept of topological crystal. The corresponding higher-order topological surface theory can also be systematically studied via higher-order bulk-boundary correspondence. In particular, we discover an intriguing fact that almost all topological crystals with nontrivial 2D block states are intrinsically interacting topological phases that cannot be realized in any free-fermion systems. Moreover, the crystalline equivalence principle for 3D interacting fermionic systems is also verified, with an additional subtle "twist" on the spin of fermions., Comment: 52+33 pages, 30+26 figures, comments are welcome

We propose a novel scene flow method that captures 3D motions from point clouds without relying on ground-truth scene flow annotations. Due to the irregularity and sparsity of point clouds, it is expensive and time-consuming to acquire ground-truth scene flow annotations. Some state-of-the-art approaches train scene flow networks in a self-supervised learning manner via approximating pseudo scene flow labels from point clouds. However, these methods fail to achieve the performance level of fully supervised methods, due to the limitations of point cloud such as sparsity and lacking color information. To provide an alternative, we propose a novel approach that utilizes monocular RGB images and point clouds to generate pseudo scene flow labels for training scene flow networks. Our pseudo label generation module infers pseudo scene labels for point clouds by jointly leveraging rich appearance information in monocular images and geometric information of point clouds. To further reduce the negative effect of noisy pseudo labels on the training, we propose a noisy-label-aware training scheme by exploiting the geometric relations of points. Experiment results show that our method not only outperforms state-of-the-art self-supervised approaches, but also outperforms some supervised approaches that use accurate ground-truth flows.

In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite dimensional Hilbert space in general. In this paper, we give a lattice model construction and classification for 2D interacting electronic insulators. Based on the physical picture of $\mathrm{U(1)}_f$-charge decorations, we illustrate the key idea by considering the well known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry $G_f=\mathrm{U(1)}_f \rtimes_{\rho_1,\omega_2} G$, where $\mathrm{U(1)}_f$ is the charge conservation symmetry and $\rho_1, \omega_2$ are additional data which fully characterize the group structure of $G_f$. Finally we study more examples, including the full interacting classification of 2D crystalline topological insulators., Comment: 6+11 pages, 2 figures, 3 tables

In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang and Wen, the concept of equivalence classes of fermionic local unitary(FLU) transformations was proposed to systematically understand non-chiral topological phases in 2D fermion systems and an incomplete classification was obtained. On the other hand, the physical picture of fermion condensation and its corresponding super pivotal categories give rise to a generic mathematical framework to describe fermionic topological phases of quantum matter. In particular, it has been pointed out that in certain fermionic topological phases, there exists the so-called q-type anyon excitations, which have no analogues in bosonic theories. In this paper, we generalize the Gu, Wang and Wen construction to include those fermionic topological phases with q-type anyon excitations. We argue that all non-chiral fermionic topological phases in 2+1D are characterized by a set of tensors $(N^{ij}_{k},F^{ij}_{k},F^{ijm,\alpha\beta}_{kln,\chi\delta},n_{i},d_{i})$, which satisfy a set of nonlinear algebraic equations parameterized by phase factors $\Xi^{ijm,\alpha\beta}_{kl}$, $\Xi^{ij}_{kln,\chi\delta}$, $\Omega^{kim,\alpha\beta}_{jl}$ and $\Omega^{ki}_{jln,\chi\delta}$. Moreover, consistency conditions among algebraic equations give rise to additional constraints on these phase factors which allow us to construct a topological invariant partition for an arbitrary triangulation of 3D spin manifold. Finally, several examples with q-type anyon excitations are discussed, including the Fermionic topological phase from Tambara-Yamagami category for $\mathbb{Z}_{2N}$, which can be regarded as the $\mathbb{Z}_{2N}$ parafermion generalization of Ising fermionic topological phase., Comment: 51 pages, 3 figures

A quantum spin liquid (QSL) is a novel phase of matter with long-range entanglement where localized spins are highly correlated with the vanishing of magnetic order. Such exotic quantum states provide the opportunities to develop new theoretical frameworks for many-body physics and have the potential application in realizing robust quantum computations. Here we show that a gapless QSL can naturally emerge from a deconfined quantum critical point (DQCP), which is originally proposed to describe Landau forbidden continuous phase transition between antiferromagnetic (AFM) and valence-bond solid (VBS) phases. Via large-scale tensor network simulations of a square-lattice spin-1/2 frustrated Heisenberg model, both QSL state and DQCP-type AFM-VBS transition are observed. With tuning coupling constants, the AFM-VBS transition vanishes and instead, a gapless QSL phase gradually develops in between. Remarkably, along the phase boundaries of AFM-QSL and QSL-VBS transitions, we always observe the same correlation length exponents $\nu\approx 1.0$, which is intrinsically different from the one of the DQCP-type transition, indicating new types of universality classes. Our results explicitly demonstrate a new scenario for understanding the emergence of gapless QSL from an underlying DQCP. The discovered QSL phase survives in a large region of tuning parameters and we expect its experimental realizations in solid state materials or quantum simulators.

Graph representations of a target domain often project it to a set of entities (nodes) and their relations (edges). However, such projections often miss important and rich information. For example, in graph representations used in missing value imputation, items - represented as nodes - may contain rich textual information. However, when processing graphs with graph neural networks (GNN), such information is either ignored or summarized into a single vector representation used to initialize the GNN. Towards addressing this, we present CoRGi, a GNN that considers the rich data within nodes in the context of their neighbors. This is achieved by endowing CoRGi's message passing with a personalized attention mechanism over the content of each node. This way, CoRGi assigns user-item-specific attention scores with respect to the words that appear in an item's content. We evaluate CoRGi on two edge-value prediction tasks and show that CoRGi is better at making edge-value predictions over existing methods, especially on sparse regions of the graph.

It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking by topological orders. In this work, we systematically study enforced breaking of a general finite group $G_f$ by a class of topological orders, namely 0D, 1D and 2D fermionic invertible topological orders. Mathematically, the symmetry group $G_f$ is a central extension of a bosonic group $G$ by the fermion parity group $Z_2^f$, characterized by a 2-cocycle $\lambda$ $\in H^2(G,Z_2)$. With some minor assumptions and for given $G$ and $\lambda$, we are able to obtain a series of criteria on the existence or non-existence of enforced symmetry breaking by the fermionic invertible topological orders. Using these criteria, we discover many examples that are not known previously. For 2D systems, we define the physical quantities to describe symmetry-enriched invertible topological orders and derive some obstruction functions using both fermionic and bosonic languages. In the latter case which is done via gauging the fermion parity, we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. We also study enforced breaking of the continuous group $SU_f(N)$ by 2D invertible topological orders through a different argument., Comment: 29 pages, 4 figures, 6 tables, comment and suggestion are welcome

Let $\Gamma$ be a non-uniform lattice in $\operatorname{PSL}(2,\mathbb R)$. In this note, we show that there exists a constant $\gamma_0>0$ such that for any $0<\gamma<\gamma_0$, any one-parametrer unipotent subgroup $\{u(t)\}_{t\in\mathbb R}$ and any $p\in\operatorname{PSL}(2,\mathbb R)/\Gamma$ which is not $u(t)$-periodic, the orbit $\{u(n^{1+\gamma})p:n\in\mathbb N\}$ is dense in $\operatorname{PSL}(2,\mathbb R)/\Gamma$. We also prove that there exists $N\in\mathbb N$ such that for the set $\Omega(N)$ of $N$-almost primes, and for any $p\in\operatorname{PSL}(2,\mathbb R)/\Gamma$ which is not $u(t)$-periodic, the orbit $\{u(x)p:x\in\Omega(N)\}$ is dense in $\operatorname{PSL}(2,\mathbb R)/\Gamma$., Comment: Correct some arguments in the previous version

In this work, we study the prospect of detecting the stochastic gravitational-wave background with the TianQin Observatory. We consider sources of both astrophysical-origin and cosmological-origin, including stellar-mass binary black holes, binary neutron stars, Galactic white dwarves, inflation, first-order phase transitions, and cosmic defects. For the detector configurations, we consider TianQin, TianQin I+II, and TianQin + LISA. We study the detectability of stochastic gravitational-wave backgrounds with both the cross correlation and null channel methods, and present the corresponding power-law integrated sensitivity curves. We introduce the definition of the "joint foreground" with a network of detectors. With the joint foreground, the number of resolved double white dwarves in the Galaxy will be increased by 5$-$22\% compared with a simple combination of individual detectors. The astrophysical background is expected to be detectable with a signal-to-noise ratio of 100 after 5 years of operation and dominated by the extragalactic double white dwarves. On the other hand, due to the uncertain nature of underlying models, we can only estimate the detection capability of the cosmological background for specific cases., Comment: 20 pages, 10 figures, update to match published version

We prove that certain sequences of periodic orbits of the diagonal group in the space of lattices equidistribute. As an application we obtain new information regarding the sequence of best approximations to certain vectors with algebraic coordinates. In order to prove these results we generalize the seminal work of Eskin Mozes and Shah about the equidistribution of translates of periodic measures from the real case to the S-arithmetic case., Comment: Minor changes on Theorem 1.2 and Theorem 1.4; add a proof of Theorem 1.5

False discovery rate (FDR) controlling procedures provide important statistical guarantees for the replicability in signal identification based on multiple hypotheses testing. In many fields of study, FDR controlling procedures are used in high-dimensional (HD) analyses to discover features that are truly associated with the outcome. In some recent applications, data on the same set of candidate features are independently collected in multiple different studies. For example, gene expression data are collected at different facilities and with different cohorts, to identify the genetic biomarkers of multiple types of cancers. These studies provide us opportunities to identify signals by considering information from different sources (with potential heterogeneity) jointly. This paper is about how to provide FDR control guarantees for the tests of union null hypotheses of conditional independence. We present a knockoff-based variable selection method (\textit{Simultaneous knockoffs}) to identify mutual signals from multiple independent data sets, providing exact FDR control guarantees under finite sample settings. This method can work with very general model settings and test statistics. We demonstrate the performance of this method with extensive numerical studies and two real data examples.

Dark matter is one of the deepest mystery of the universe. So far there is no natural explanation why the dark matter should exist and even dominate the universe. In this paper, we begin with a 3+1D topological gravity theory which is super renormalizable with vanishing beta functions, then we argue that Einstein gravity can emerge by condensing loop-like excitation from the underlying topological gravity theory. In the meanwhile, the uncondensed loop-like excitations serves as a natural candidate of dark matter and a generalized Einstein equation can be derived in the presence of loop-source(dark matter) background. Surprisingly, we find that such kind of dark matter will not contribute to scalar curvature, however, it will become a source of torsion. Finally, we derive the generalized Einstein equation in the presence of Dirac field. Very different from the usual Einstein-Carton theory, our theory further predicts that any type of normal matter, including Dirac field will not produce torsion. All these unique predictions can be tested by future experiments. Our framework suggests that topological invariant principle might play a more profound role than the well-known general covariance principle, especially towards understanding the nature of dark matter and quantum gravity in 3+1D., Comment: 24 pages, comments and suggestions are welcome

We propose a novel scene flow estimation approach to capture and infer 3D motions from point clouds. Estimating 3D motions for point clouds is challenging, since a point cloud is unordered and its density is significantly non-uniform. Such unstructured data poses difficulties in matching corresponding points between point clouds, leading to inaccurate flow estimation. We propose a novel architecture named Sparse Convolution-Transformer Network (SCTN) that equips the sparse convolution with the transformer. Specifically, by leveraging the sparse convolution, SCTN transfers irregular point cloud into locally consistent flow features for estimating continuous and consistent motions within an object/local object part. We further propose to explicitly learn point relations using a point transformer module, different from exiting methods. We show that the learned relation-based contextual information is rich and helpful for matching corresponding points, benefiting scene flow estimation. In addition, a novel loss function is proposed to adaptively encourage flow consistency according to feature similarity. Extensive experiments demonstrate that our proposed approach achieves a new state of the art in scene flow estimation. Our approach achieves an error of 0.038 and 0.037 (EPE3D) on FlyingThings3D and KITTI Scene Flow respectively, which significantly outperforms previous methods by large margins., Comment: Accepted to the 36th AAAI Conference on Artificial Intelligence (AAAI 2022)

Iron selenide (FeSe) is an iron-based superconductor which shows unique properties, including strongly anisotropic superconducting gap, paramagnetism in undoped compound and extremely small Fermi pocket size. In this work, we demonstrate that the sizes of electron and hole pockets in FeSe monolayer become much smaller than those in bulk. The Fermi energy is in the order of a few meV and can be fine-tuned by the thickness of graphene layers underneath. Despite the low carrier density, the FeSe monolayers grown on trilayer or multi-layer graphene are superconducting. The superconducting gap size is sensitive to the Fermi energy of the hole band. Remarkably, the FeSe monolayer provides the opportunity to study the physics in the crossover regime where the Fermi energy and superconducting gap are comparable to each other.

The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems., Comment: 39+37 pages, 10+13 figures, 3+1 tables, all comments and suggestions are very welcome

We accurately simulate the phase diagram and critical behavior of the $q$-state clock model on the square lattice by using the state-of-the-art loop optimization for tensor network renormalzation(loop-TNR) algorithm. The two phase transition points for $q \geq 5$ are determined with very high accuracy. Furthermore, by computing the conformal scaling dimensions, we are able to accurately determine the compactification radius $R$ of the compactified boson theories at both phase transition points. In particular, the compactification radius $R$ at high-temperature critical point is precisely the same as the predicted $R$ for Berezinskii-Kosterlitz-Thouless (BKT) transition. Moreover, we find that the fixed point tensors at high-temperature critical point also converge(up to numerical errors) to the same one for large enough $q$ and the corresponding operator product expansion(OPE) coefficient of the compactified boson theory can also be read out directly from the fixed point tensor., Comment: 16 pages, 31 figures