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We explore a large $N$ generalization of the Kitaev model on the honeycomb lattice with a simple nearest-neighbor interacting Hamiltonian. In particular, we focus on the $\mathbb{Z}_4$ case with isotropic couplings, which is characterized by an exact $\mathbb{Z}_4$ one-form symmetry. Guided by symmetry considerations and an analytical study in the single chain limit, on the infinitely long cylinders, we find the model is gapped with an extremely short correlation length. Combined with the $\mathbb{Z}_4$ one-form symmetry, this suggests the model is topologically ordered. To pin down the nature of this phase, we further study the model on both finite and infinitely long strips, where we consistently find a $c=1$ conformal field theory (CFT) description, suggesting the existence of chiral edge modes described by a free boson CFT. Further evidence is found by studying the dimer correlators on infinitely long strips. We find the dimer correlation functions show a power-law decay with the exponent close to 2 on the boundary of the strip, while decay much faster in the bulk. Combined with the topological entanglement entropy extracted from cylinder geometry, we identify the spin liquid is chiral and supports a $\mathrm{U}(1)_{-8}$ chiral topological order. A unified perspective for all $\mathbb{Z}_N$ type Kitaev models is also discussed., Comment: 10 pages, 5 figures

The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS), two-dimensional tensor network states, remains largely underexplored. We present a novel framework for understanding 1-form symmetries within tensor networks, specifically focusing on the derivation of algebraic relations for symmetry matrices on the PEPS virtual legs. Our results reveal that 1-form symmetries impose stringent constraints on tensor network representations, leading to distinct anomalous braiding phases carried by symmetry matrices. We demonstrate how these symmetries influence the ground state and tangent space in PEPS, providing new insights into their physical implications for enhancing ground state optimization efficiency and characterizing the 1-form symmetry structure in excited states., Comment: 6 pages, 1 figure. In memory of T. M. Rice for his invaluable teaching on the physics of strongly correlated systems

Magnetic skyrmions emerge as promising quasi-particles for encoding information in nextgeneration spintronic devices. Their innate flexibility in shape is essential for the applications although they were often ideally treated as rigid particles. In this work, we investigated the voltagecontrolled uniform strain mediated dynamics of deformed skyrmions in heterostructures with a flower-shaped magnetic nanostructure, using micromagnetic simulations. The simulated results revealed the possible states of isolated skyrmion nucleated in the nanostructure, which can be mutually switched by applying suitable in-plane strain pulses. In addition, it was found that the skyrmion motions are driven by the emerging internal forces and strain force, which originate from the asymmetric deformation of skyrmion structures. Furthermore, an analytical model of deformed skyrmions was proposed to interpret the dependences of internal forces and strain force on the asymmetric deformation of skyrmion, with some formulae derived for these forces in a semi-analytical approach. Further calculations based on these formulae verified the forces appearing in the skyrmion motion, with the resulting forces showing consistence with the simulated data. This suggested that our semi-analytical model successfully captures the main physics responsible for the motion of deformed skyrmion in the nanostructure. Our work extends the understanding of the mechanics emerging in deformed skyrmion, and provides an effective approach for deterministic manipulation of deformed skyrmion motion via strain forces and internal forces, which may be instructive to design of skyrmion-based spintronic devices.

Deep learning has deeply changed the paradigms of many research fields. At the heart of chemical and physical sciences is the accurate ab initio calculation of many-body wavefunction, which has become one of the most notable examples to demonstrate the power of deep learning in science. In particular, the introduction of deep learning into quantum Monte Carlo (QMC) has significantly advanced the frontier of ab initio calculation, offering a universal tool to solve the electronic structure of materials and molecules. Deep learning QMC architectures were initial designed and tested on small molecules, focusing on comparisons with other state-of-the-art ab initio methods. Methodological developments, including extensions to real solids and periodic models, have been rapidly progressing and reported applications are fast expanding. This review covers the theoretical foundation of deep learning QMC for solids, the neural network wavefunction ansatz, and various of other methodological developments. Applications on computing energy, electron density, electric polarization, force and stress of real solids are also reviewed. The methods have also been extended to other periodic systems and finite temperature calculations. The review highlights the potentials and existing challenges of deep learning QMC in materials chemistry and condensed matter physics.

Moir\'e superlattice designed in stacked van der Waals material provides a dynamic platform for hosting exotic and emergent condensed matter phenomena. However, the relevance of strong correlation effects and the large size of moir\'e unit cells pose significant challenges for traditional computational techniques. To overcome these challenges, we develop an unsupervised deep learning approach to uncover electronic phases emerging from moir\'e systems based on variational optimization of neural network many-body wavefunction. Our approach has identified diverse quantum states, including novel phases such as generalized Wigner crystals, Wigner molecular crystals, and previously unreported Wigner covalent crystals. These discoveries provide insights into recent experimental studies and suggest new phases for future exploration. They also highlight the crucial role of spin polarization in determining Wigner phases. More importantly, our proposed deep learning approach is proven general and efficient, offering a powerful framework for studying moir\'e physics.

We investigate a fractional Chern insulator (FCI) candidate arising from Moir\'e bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle $\phi\approx 1.608^{\circ}$ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moir\'e Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction $\nu=1/5$. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system., Comment: 14 pages, 9 figures

The integration of deep neural networks with the Variational Monte Carlo (VMC) method has marked a significant advancement in solving the Schr\"odinger equation. In this work, we enforce spin symmetry in the neural network-based VMC calculation with modified optimization target. Our method is designed to solve for the ground state and multiple excited states with target spin symmetry at a low computational cost. It predicts accurate energies while maintaining the correct symmetry in strongly correlated systems, even in cases where different spin states are nearly degenerate. Our approach also excels at spin-gap calculations, including the singlet-triplet gap in biradical systems, which is of high interest in photochemistry. Overall, this work establishes a robust framework for efficiently calculating various quantum states with specific spin symmetry in correlated systems, paving the way for novel discoveries in quantum science.

Whether face processing depends on unique, domain-specific neurocognitive mechanisms or domain-general object recognition mechanisms has long been debated. Directly testing these competing hypotheses in humans has proven challenging due to extensive exposure to both faces and objects. Here, we systematically test these hypotheses by capitalizing on recent progress in convolutional neural networks (CNNs) that can be trained without face exposure (i.e., pre-trained weights). Domain-general mechanism accounts posit that face processing can emerge from a neural network without specialized pre-training on faces. Consequently, we trained CNNs solely on objects and tested their ability to recognize and represent faces as well as objects that look like faces (face pareidolia stimuli).... Due to the character limits, for more details see in attached pdf, Comment: 31 pages, 5 Figures

Transition metal dichalcogenides (TMDs) are a class of two-dimensional (2D) materials been widely studied for emerging electronic properties. In this work, we use computational simulations to examine the water adsorption on TMDs systematically and the wetting property of WSe2 specifically. We start with density functional theory (DFT) based random phase approximation (RPA), assessing the performance of exchange-correlation functionals and comparing water adsorption on various TMDs. We also perform \textit{ab initio} molecular dynamics (AIMD) simulations on tungsten diselenide (WSe$_2$), from which we find that the distribution of interfacial water is sensitive to the exchange-correlation functional selected and a reasonable choice leads to a diffusive contact layer where water molecules prefer the "flat" configuration. Classical molecular dynamics (MD) simulations of water droplets on surfaces using appropriately parameterized water-surface interaction further confirm the dependence of water contact angle on the interaction and the interfacial water structure reproduced by different DFT functionals. Our study highlights the sensitivity of wetting to the water-substrate interaction and provides a starting point for a more accurate theoretical investigation of water-TMD interfaces.

While gauge symmetry is a well-established requirement for representing topological orders in projected entangled-pair state (PEPS), its impact on the properties of low-lying excited states remains relatively unexplored. Here we perform PEPS simulations of low-energy dynamics in the Kitaev honeycomb model, which supports fractionalized gauge flux (vison) excitations. We identify gauge symmetry emerging upon optimizing an unbiased PEPS ground state. Using the PEPS adapted local mode approximation, we further classify the low-lying excited states by discerning different vison sectors. Our simulations of spin and spin-dimer dynamical correlations establish close connections with experimental observations. Notably, the selection rule imposed by the locally conserved visons results in nearly flat dispersions in momentum space for excited states belonging to the 2-vison or 4-vison sectors., Comment: 8 pages, 5 figures

In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and the principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be more sensitive to potential departures from general relativity (GR). We extend previous works by employing Bayesian parameter estimation and performing both tests with injections of GR and injections of subtle GR-violated signals. We also apply multi-parameter tests with PCA in the phenomenological test of GW propagation. This work complements previous works and further demonstrates the enhancement provided by the PCA method. Considering a supermassive black hole binary system as the GW source, we show that subtle departures will be more obvious in posteriors of PCA parameters. The departures less than $1\sigma$ in original parameters can yield significant departures in first 5 dominant PCA parameters., Comment: 21 pages, 10 figures; Update to match the published version

This paper provides an overview of three notable approaches for detecting anomalies in spatio-temporal data. The three review methods are selected from the framework of multivariate statistical process control (SPC), scan statistics, and tensor decomposition. For each method, we first demonstrate its technical intricacies and then apply it to a real-world dataset, which is 300 images of solar activities collected by satellite. Our findings reveal that these methods possess distinct strengths. Specifically, scan statistics excel at identifying clustered anomalies, multivariate SPC is effective in detecting sparse anomalies, and tensor decomposition is adept at identifying anomalies exhibiting desirable patterns, such as temporal circularity. We emphasize the importance of customizing the selection of these methods based on the specific characteristics of the dataset and the analysis objectives.

In single unit-cell FeSe grown on SrTiO3, the superconductivity transition temperature features a significant enhancement. Local phonon modes at the interface associated with electron-phonon coupling may play an important role in the interface-induced enhancement. However, such phonon modes have eluded direct experimental observations. Indeed, the complicated atomic structure of the interface brings challenges to obtain the accurate structure-phonon relation knowledge from either experiment or theory, thus hindering our understanding of the enhancement mechanism. Here, we achieve direct characterizations of atomic structure and phonon modes at the FeSe/SrTiO3 interface with atomically resolved imaging and electron energy loss spectroscopy in a scanning transmission electron microscope. We find several phonon modes highly localized (~1.3 nm) at the unique double layer Ti-O termination at the interface, one of which (~ 83 meV) engages in strong interactions with the electrons in FeSe based on ab initio calculations. The electron-phonon coupling strength for such a localized interface phonon with short-range interactions is comparable to that of Fuchs-Kliewer (FK) phonon mode with long-rang interactions. Thus, our atomic-scale study provides new insights into understanding the origin of superconductivity enhancement at the FeSe/SrTiO3 interface.

Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network architectures, the training becomes more difficult and expensive, which may have a counterproductive effect on the accuracy of calculation. In this work, we propose to make use of the training data to perform variance extrapolation when using neural-network ansatz in variational Monte Carlo. We show that this approach can speed up the convergence and surpass the ansatz limitation to obtain an improved estimation of the energy. Moreover, variance extrapolation greatly enhances the error cancellation capability, resulting in significantly improved relative energy outcomes, which are the keys to chemistry and physics problems.

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating function approach for tensor network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-$1/2$ transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-$1/2$ $J_1$-$J_2$ model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multi-particle excitations., Comment: 13 pages, 6 figures

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.

Ab initio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated functionals. Here we employ a neural network wavefunction ansatz combined with quantum Monte Carlo to incorporate correlations into polarization calculations. On a variety of systems, including isolated atoms, one-dimensional chains, two-dimensional slabs, and three-dimensional cubes, the calculated results outperform conventional density functional theory and are consistent with the most accurate calculations and experimental data. Furthermore, we have studied the out-of-plane dielectric constant of bilayer graphene using our method and re-established its thickness dependence. Overall, this approach provides a powerful tool to consider electron correlation in the modern theory of polarization.