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Quantum many-body systems are challenging targets for computational physics due to their large degrees of freedom. The tensor networks, particularly Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), effectively represent these systems on two-dimensional lattices. However, the technical complexity of TPS/PEPS-based coding is often too much for researchers to handle. To reduce this problem, we developed TeNeS (Tensor Network Solver). This paper introduces TeNeS-v2, which extends TeNeS with real-time and finite temperature simulations, providing deeper insights into quantum many-body systems. We detail the new algorithms, input/output design, and application examples, demonstrating TeNeS-v2's applicability to various quantum spin and Bose models on two-dimensional lattices., Comment: 10 pages, 8 figures

We propose a multi-impurity method for the bond-weighted tensor renormalization group (BWTRG) to compute the higher-order moment of physical quantities in a two-dimensional system. The replacement of the bond weight with an impurity matrix in a bond-weighted triad tensor network represents a physical quantity such as the magnetization and the energy. We demonstrate that the accuracy of the proposed method is much higher than the conventional tensor renormalization group for the Ising model and the 5-state Potts model. Furthermore, we perform the finite-size scaling analysis and observe that the dimensionless quantity characterizing the structure of the fixed point tensor satisfies the same scaling relation in the critical region as the Binder parameter. The estimated critical temperature dependence on the bond dimension indicates that the exponent relating the correlation length to the bond dimension varies continuously with respect to the BWTRG hyperparameter. We find that BWTRG with the optimal hyperparameter is more efficient in terms of computational time than alternative approaches based on the matrix product state in estimating the critical temperature., Comment: 9 pages, 10 figures

Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of a particle trapping in a potential well, i.e., survival probability in the process carrying of the particle for a given length within a given fixed time. For the actual motion of conveyance, we need to accelerate the particle to move and then decelerate it to stop at the destination. First, the relaxation of the survival probability in a constant acceleration rate is studied in detail by direct numerical calculation, the Wentzel-Kramers-Brillouin method, and a method of the resonance states. The survival probability was found to show an exponential decay in a long time, which is analyzed from a viewpoint of eigenvalue problem. An important source of dropoff comes from a non-analytic change of velocity at the starting point. When the rested particle begins to move, the ground state of the rest frame is redistributed to eigenstates of the moving frame, and then each eigenstate of the moving frame evolves in time. The dephasing of wave functions of the distributed populations reduces the probability of successful conveyance. In general, a smooth start gives a small initial disturbance but requires a large acceleration during the process to reach the destination in the fixed time which causes a larger dropoff in the process. Considering these conflicting facts, we study the survival probability in concrete conveyance schemes. We observe the time evolution of the trapped probability and the population distribution during the conveyance process. In cases that the potential well has several bound states, we propose a method to select the particle trapped at the ground state by making use of the difference of survival probabilities of bound states., Comment: 21 pages, 17 figures

Context. Solar filament eruptions usually appear to occur in association with the sudden explosive release of magnetic energy accumulated in long-lived arched magnetic structures. It is the released energy that occasionally drives fast-filament eruptions that can be source regions of coronal mass ejections. Aim. The goal of this paper is to investigate the dynamic processes of a fast-filament eruption by using unprecedented high-resolution full-disk H$\alpha$ imaging spectroscopy observations. Methods. The whole process of the eruption was captured in a wide spectral window of the H$\alpha$ line ($\pm9.0$ A). Applying the "cloud model" and obtaining two dimensional optical thickness spectra we derive the Doppler velocity, the true eruption profiles (height, velocity, and acceleration), and the trajectory of the filament eruption in 3D space. Results. The Doppler velocity maps show that the filament was predominantly blue-shifted. During the main and final process of the eruption, strongly blue-shifted materials are manifested traveling with velocities exceeding $250~km/s$. The spectral analysis further revealed that the erupting filament is made of multiple components, some of which were Doppler-shifted approximately to $-300 ~km/s$. It is found that the filament eruption attains a maximum true velocity and acceleration of about $600~km/s$ and $2.5~km/s^2$, respectively, and its propagation direction deviates from the radial direction. On the other hand, downflows manifested as red-shifted plasma close to the footpoints of the erupting filament move with velocities $45-125~ km/s$. We interpret these red-shifted signatures as draining material, and therefore mass loss of the filament that has implications for the dynamic and the acceleration process of the eruption. Furthermore, we have estimated the total mass of the H$\alpha$ filament resulting in $\sim$$5.4\times10^{15}g$., Comment: Accepted for publication in Astronomy & Astrophysics

Using the nuclear norm regularization techniques on tensor network renormalization algorithm, we study the phase diagram, the critical behavior and the duality property of the antiferromagnetic 6-state clock model on the Union Jack lattice. We find that this model undergoes multiple phase transitions; there is the Berezinskii-Kosterlitz-Thouless, $Z_{6}$ symmetry breaking and chiral transition with decreasing temperature. Furthermore, we provide convincing numerical evidence that its quasi-long range order is well explained by the compactified boson conformal field theory (CFT) and the chiral transition is in perfect agreement with the Ising CFT, including central charge, scaling dimension spectrum, and operator product expansion coefficients., Comment: 12 pages, 8 figures

We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity $z$, an aligning dimer-dimer interaction $u$ that favors columnar order, and an attractive dimer-dimer interaction $v$ between two adjacent dimers that lie on the same principal axis of the lattice. The Monte Carlo simulations of finite size systems rely on our grand-canonical generalization of the dimer worm algorithm, while the tensor network computations are based on a uniform matrix product ansatz for the eigenvector of the row-to-row transfer matrix that work directly in the thermodynamic limit. The phase diagram has nematic, columnar order and fluid phases, and a nonzero temperature multicritical point at which all three meet. For any fixed $v/u < \infty$, we argue that this multicritical point continues to be located at a nonzero hole fugacity $z_{\rm mc}(v/u) > 0$; our numerical results confirm this theoretical expectation but find that $z_{\rm mc}(v/u) \to 0$ very rapidly as $v/u \to \infty$. Our numerical results also confirm the theoretical expectation that the corresponding multicritical behavior is in the universality class of the four-state Potts multicritical point on critical line of the two-dimensional Ashkin-Teller model., Comment: 12 pages, 12 figures

Recent substantial advances of molecular targeted oncology drug development is requiring new paradigms for early-phase clinical trial methodologies to enable us to evaluate efficacy of several subtypes simultaneously and efficiently. The concept of the basket trial is getting of much attention to realize this requirement borrowing information across subtypes, which are called baskets. Bayesian approach is a natural approach to this end and indeed the majority of the existing proposals relies on it. On the other hand, it required complicated modeling and may not necessarily control the type 1 error probabilities at the nominal level. In this paper, we develop a purely frequentist approach for basket trials based on one-sample Mantel-Haenszel procedure relying on a very simple idea for borrowing information under the common treatment effect assumption over baskets. We show that the proposed estimator is consistent under two limiting models of the large strata and sparse data limiting models (dually consistent) and propose dually consistent variance estimators. The proposed Mantel-Haenszel estimators are interpretable even if the common treatment assumptions are violated. Then, we can design basket trials in a confirmatory matter. We also propose an information criterion approach to identify effective subclass of baskets.

We study the ground-state phase diagram of a spin-$\frac{1}{2}$ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, $J_\perp$ and $J_\times$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime $J_\perp\approx 2J_\times$, especially for ferromagnetic $J_{\perp, \times}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and obtain a rich phase diagram. The diagram includes four gapped featureless phases with no symmetry breaking: the rung singlet (RS) and Haldane phases as well as their twisted variants, the RS* and Haldane* phases, which are all distinct in the presence of certain symmetries. Significantly, the Haldane-CD transition point in the isotropic model turns out to be a crossing point of two transition lines in the XXZ model, and the stripe N\'eel and RS* phases appear between these lines. This indicates a nontrivial interplay between the effective dimer attraction and the exchange anisotropy. In the easy-plane regime, the four featureless phases and two critical phases are found to compete in a complex manner depending on the signs of $J_{\perp, \times}$.

TeNeS (Tensor Network Solver) is a free/libre open-source software program package for calculating two-dimensional many-body quantum states based on the tensor network method and the corner transfer matrix renormalization group (CTMRG) method. This package calculates ground-state wavefunctions for user-defined Hamiltonians and evaluates user-defined physical quantities such as magnetization and correlation functions. For certain predefined models and lattices, there is a tool that makes it easy to generate input files. TeNeS uses an OpenMP/MPI hybrid parallelized tensor operation library and thus can perform large-scale calculations using massively parallel machines., Comment: 16 pages, 10 figures

We study a non-monotonic behavior of the Binder parameter, which appears in the discrete spin systems. We show that the Binder parameters of the Potts model are non-monotonic for $q=3$ and $4$, while they are monotonic for the Ising case ($q=2$). Using the Fortuin-Kasteleyn graph representation, we find that the improved estimator of the Binder parameter consists of two terms with values only in high- and low-temperature regions. The non-monotonic behavior is found to originate from the low-temperature term. With the appropriately defined order parameter, we can reduce the influence of the low-temperature term, and as a result, the non-monotonic behavior can also be reduced. We propose new definitions of the order parameter, which reduces or eliminates the non-monotonic behavior of the Binder parameter in a system for which the improved estimator of the Binder parameter is unknown., Comment: 20 pages, 12 figures, added new results

We study a spin-1/2 XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS* and Haldane* phases, in which twisted singlet pairs are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge c=1 occur between the featureless phases and between the ordered phases while Ising transitions with c=1/2 occur between the featureless and ordered phases. The two types of transition lines cross at the SU(2)-symmetric point, where the criticality is described by the SU(2)_2 Wess-Zumino-Witten theory with c=3/2. The RS-Haldane* and RS*-Haldane transitions give examples of topological phase transitions. Interestingly, the RS* and Haldane* phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries., Comment: 17 pages, 22 figures

We propose a new class of tight-binding systems of interacting bosons with a flat band, which are exactly solvable in the sense that one can explicitly write down the unique ground state. The ground state is expressed in terms of local creation operators, and apparently resembles that of a Mott insulator. Based on an exact representation in terms of a classical loop-gas model, we conjecture that the ground state may exhibit quasi Bose-Einstein condensation (BEC) or genuine BEC in dimensions two and three or higher, respectively, still keeping Mott insulator-like character. Our Monte Carlo simulation of the loop-gas model strongly supports this conjecture, i.e., the ground state undergoes a Kosterlitz-Thouless transition and exhibits quasi BEC in two dimensions., Comment: 14 pages, 13 figures. The format has been changed and some discussions has been added in vers. 5. Further improvements and a new figure (Fig.2) in vers. 6. There is a 22.5 minutes video in which the main results of the paper are described. See https://youtu.be/ef9x11C1cVg

We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities., Comment: 8 pages, 5 figures

We present a detailed three-dimensional (3D) view of a prominence eruption, coronal loop expansion, and coronal mass ejections (CMEs) associated with an M4.4 flare that occurred on 2011 March 8 in the active region NOAA 11165. Full-disk H$\alpha$ images of the flare and filament ejection were successfully obtained by the Flare Monitoring Telescope (FMT) following its relocation to Ica University, Peru. Multiwavelength observation around the H$\alpha$ line enabled us to derive the 3D velocity field of the H$\alpha$ prominence eruption. Features in extreme ultraviolet were also obtained by the Atmospheric Imager Assembly onboard the {\it Solar Dynamic Observatory} and the Extreme Ultraviolet Imager on board the {\it Solar Terrestrial Relations Observatory - Ahead} satellite. We found that, following collision of the erupted filament with the coronal magnetic field, some coronal loops began to expand, leading to the growth of a clear CME. We also discuss the succeeding activities of CME driven by multiple interactions between the expanding loops and the surrounding coronal magnetic field., Comment: 17 pages, 9 figures; accepted for publication in PASJ

We investigate a quantum phase transition between a Neel phase and a valence bond solid (VBS) phase, in each of which a different Z2 symmetry is broken, in a spin-1/2 two-leg XXZ ladder with a four-spin interaction. The model can be viewed as a one-dimensional variant of the celebrated J-Q model on a square lattice. By means of variational uniform matrix product state calculations and an effective field theory, we determine the phase diagram of the model, and present evidences that the Neel-VBS transition is continuous and belongs to the Gaussian universality class with the central charge c=1. In particular, the critical exponents $\beta, \eta,$ and, $\nu$ are found to satisfy the constraints expected for a Gaussian transition within numerical accuracy. These exponents do not detectably change along the phase boundary while they are in general allowed to do so for the Gaussian class., Comment: 14 pages, 11 figures

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration is unnecessary, which is a time-consuming part of other methods with global optimization. In addition, a further approximation reducing the order of the computational cost of contraction for the calculation of the coarse-grained tensor is proposed. The computational time of our algorithm in two dimensions scales as the sixth power of the bond dimension while the higher-order tensor renormalization group and the higher-order second renormalization group methods have the seventh power. We perform benchmark calculations in the Ising model on the square lattice and show that the time-to-solution of the proposed algorithm is faster than that of other methods., Comment: 6 pages, 9 figures

The solar group at the National Astronomical Observatory of Japan is conducting synoptic solar observations with the Solar Flare Telescope. While it is a part of a long-term solar monitoring, contributing to the study of solar dynamo governing solar activity cycles, it is also an attempt at contributing to space weather research. The observations include imaging with filters for H$\alpha$, Ca K, G-band, and continuum, and spectropolarimetry at the wavelength bands including the He I 1083.0 nm / Si I 1082.7 nm and the Fe I 1564.8 nm lines. Data for the brightness, Doppler signal, and magnetic field information of the photosphere and the chromosphere are obtained. In addition to monitoring dynamic phenomena like flares and filament eruptions, we can track the evolution of the magnetic fields that drive them on the basis of these data. Furthermore, the magnetic field in solar filaments, which develops into a part of the interplanetary magnetic cloud after their eruption and occasionally hits the Earth, can be inferred in its pre-eruption configuration. Such observations beyond mere classical monitoring of the Sun will hereafter become crucially important from the viewpoint of the prediction of space weather phenomena. The current synoptic observations with the Solar Flare Telescope is considered to be a pioneering one for future synoptic observations of the Sun with advanced instruments., Comment: 18 pages, 6 figures

We numerically obtain the conformal spectrum of several classical spin models on a two-dimensional lattice with open boundaries, for every boundary fixed point obtained by the Cardy's derivation [J. L. Cardy, Nucl. Phys. B 324, 581 (1989)]. In order to extract accurate conformal data, we implement the tensor network renormalization algorithm [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] extended so as to be applicable to a square lattice with open boundaries. We successfully compute the boundary conformal spectrum consistent with the underlying boundary conformal field theories (BCFTs) for the Ising, tri-critical Ising, and 3-state Potts models on the lattice, which allows us to confirm the validity of the BCFT analyses for the surface critical behaviors of those lattice models., Comment: 12 pages, 12 figures

A utility-based Bayesian population finding (BaPoFi) method was proposed by Morita and M\"uller (2017, Biometrics, 1355-1365) to analyze data from a randomized clinical trial with the aim of identifying good predictive baseline covariates for optimizing the target population for a future study. The approach casts the population finding process as a formal decision problem together with a flexible probability model using a random forest to define a regression mean function. BaPoFi is constructed to handle a single continuous or binary outcome variable. In this paper, we develop BaPoFi-TTE as an extension of the earlier approach for clinically important cases of time-to-event (TTE) data with censoring, and also accounting for a toxicity outcome. We model the association of TTE data with baseline covariates using a semi-parametric failure time model with a P\'olya tree prior for an unknown error term and a random forest for a flexible regression mean function. We define a utility function that addresses a trade-off between efficacy and toxicity as one of the important clinical considerations for population finding. We examine the operating characteristics of the proposed method in extensive simulation studies. For illustration, we apply the proposed method to data from a randomized oncology clinical trial. Concerns in a preliminary analysis of the same data based on a parametric model motivated the proposed more general approach., Comment: 25 pages, 4 figures

We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate that the tensors representing the boundary in our algorithm exhibit the fixed point structures just as bulk tensors in previous TRG algorithms. At criticality, the scale-invariant boundary fixed point tensors have the information of the conformal tower, which is described by the underlying boundary conformal field theory., Comment: 9 pages, some useful figs are added

We present efficient algorithms to generate a bit string in which each bit is set with arbitrary probability. By adopting a hybrid algorithm, i.e., a finite-bit density approximation with correction techniques, we achieve 3.8 times faster random bit generation than the simple algorithm for the 32-bit case and 6.8 times faster for the 64-bit case. Employing the developed algorithm, we apply the multispin coding technique to one-dimensional bond-directed percolation. The simulations are accelerated by up to a factor of 14 compared with an optimized scalar implementation. The random bit string generation algorithm proposed here is applicable to general Monte Carlo methods., Comment: 9 pages, 7 figures

A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A systematic summation scheme provides coarse-grained tensors including multiple impurities. Our method is compared with the Monte Carlo method on the two-dimensional Potts model. While the nature of the transition of the $q$-state Potts model has been known for a long time owing to the analytical arguments, a clear numerical confirmation has been difficult due to extremely long correlation length in the weakly first-order transitions, e.g., for $q=5$. A jump of the Binder ratio precisely determines the transition temperature. The finite-size scaling analysis provides critical exponents and distinguishes the weakly first-order and the continuous transitions., Comment: 8 pages, 9 figures

We investigate the first-order phase transitions of the $q$-state Potts models with $q = 5, 6, 7$, and $8$ on the two-dimensional square lattice, using Monte Carlo simulations. At the very weakly first-order transition of the $q=5$ system, the standard data-collapse procedure for the order parameter, carried out with results for a broad range of system sizes, works deceptively well and produces non-trivial critical exponents different from the trivial values expected for first-order transitions. However, a more systematic study reveals significant drifts in the `pseudo-critical' exponents as a function of the system size. For this purpose, we employ two methods of analysis: the data-collapse procedure with narrow range of the system size, and the Binder-cumulant crossing technique for pairs of system sizes. In both methods, the estimates start to drift toward the trivial values as the system size used in the analysis exceeds a certain `cross-over' length scale. This length scale is remarkably smaller than the correlation length at the transition point for weakly first-order transitions, e.g., less than one tenth for $q=5$, in contrast to the naive expectation that the system size has to be comparable to or larger than the correlation length to observe the correct behavior. The results overall show that proper care is indispensable to diagnose the nature of a phase transition with limited system sizes., Comment: 10 pages, 7 figures. One figure has been replaced to make our claim clearer

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model., Comment: 7 pages, 6 figures. Published version

mVMC (many-variable Variational Monte Carlo) is an open-source software based on the variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. In this paper, we explain basics and user interfaces of mVMC. By using mVMC, users can perform the calculation by preparing only one input file of about ten lines for widely studied quantum lattice models, and can also perform it for general Hamiltonians by preparing several additional input files. We show the benchmark results of mVMC for the Hubbard model, the Heisenberg model, and the Kondo-lattice model. These benchmark results demonstrate that mVMC provides ground-state and low-energy-excited-state wave functions for interacting fermion systems with high accuracy., Comment: 19 pages, 8 figures, source code can be found at https://ma.issp.u-tokyo.ac.jp/en/app/518 and https://github.com/issp-center-dev/mVMC, accepted for publication in Computer Physics Communications

The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one- and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to hole doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak $d$-wave superconducting order in the ground state for the doping concentration less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25., Comment: 18 pages, 19 figures