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Naoki Kawashima

Publications and source records attributed to Naoki Kawashima.

At least 37 records · Page 2Linked to original sources
arXiv2024

Generating function for projected entangled-pair states

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.

cond-mat.str-el↗
arXiv2023

Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model

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.

cond-mat.stat-mech↗
arXiv2023

Possibility of a Topological Phase Transition in Two-dimensional $RP^3$ Model

We study by large-scale Monte Carlo simulation the $RP^3$ model, which can be regarded as an effective low-energy model of a triangular lattice Heisenberg antiferromagnet. $Z_2$ vortices appear as elementary excitations in the triangular lattice Heisenberg antiferromagnet. Such $Z_2$ vortices are ubiquitous in other frustrated Heisenberg spin systems that have noncollinear long-range orders. In this study, we investigate a possible topological phase transition driven by the binding--unbinding of $Z_2$ vortices. By extracting important degrees of freedom, we map a frustrated spin system to an effective $RP^3$ model. From large-scale Monte Carlo simulation, we obtain an order parameter and a correlation length of up to $L=16384$. Concerning the existence of a $Z_2$-vortex transition, by extrapolating the order parameter to the thermodynamics limit assuming the $Z_2$-vortex transition, we obtain a finite transition temperature as $T_v/\tilde{J} \simeq 0.25$. Our estimate of the correlation length at $T_v$ is much larger than $L=16384$, which is beyond the previous estimate obtained with the triangular lattice Heisenberg model.

cond-mat.stat-mech↗
arXiv2023

Update of $\mathcal{H}Φ$: Newly added functions and methods in versions 2 and 3

$\mathcal{H}Φ$ [$aitch$-$phi$] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal blocking preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the $ab$ $initio$ low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode $\unicode{x2014}$simplified input format in $\mathcal{H}Φ$$\unicode{x2014}$ to use these functions and methods. We explain the basics of the implemented methods and how to use them.

cond-mat.str-el↗
arXiv2023

Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary

We study the simplest quantum lattice spin model for the two-dimensional (2D) cubic ferromagnet by means of mean-field analysis and tensor network calculation. While both methods give rise to similar results in detecting related phases, the 2D infinite projected entangled-pair state (iPEPS) calculation provides more accurate values of transition points. Near the phase boundary, moreover, our iPEPS results indicate that it is more difficult to pin down the orientation of magnetic easy axes, and we interpret it as the easy-axis softening. This phenomenon implies an emergence of continuous $U(1)$ symmetry, which is indicated by the low-energy effective model and has been analytically shown by the field theory. Our model and study provide a concrete example for utilizing iPEPS near the critical region, showing that the emergent phenomenon living on the critical points can already be captured by iPEPS with a rather small bond dimension.

cond-mat.str-el↗
arXiv2023

Non-monotonic behavior of the Binder Parameter in the discrete spin systems

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.

cond-mat.stat-mech↗
arXiv2022

TeNeS: Tensor Network Solver for Quantum Lattice Systems

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.

cond-mat.str-el↗
arXiv2021

Universal and Non-Universal Correction Terms of Bose Gases in Dilute Region: a Quantum Monte Carlo Study

We study dilute gases of interacting bosons at zero-temperature in the region where the system is characterized only by the s-wave scattering length. We carry out quantum Monte Carlo simulation of the Bose Hubbard model and a continuous-space hard-core model. Fitting the extended Lee-Huang-Yang formula to the Monte Carlo results establishes the detailed mapping from the lattice model to the continuous field theory characterized only by the s-wave scattering length. Our estimate of the intrinsic s-wave scattering length $a_s$ of the Bose-Hubbard model is $a_s/a_l = 0.316(2)$ where $a_l$ is the lattice constant. It turned out that inclusion of the universal second correction term of $O(n \log n)$ makes the fitting worse while it is restored by inclusion of the non-universal third correction term, of which the existence was predicted analytically.

cond-mat.quant-gas↗
arXiv2021

Multiple magnetization plateaus induced by farther neighbor interaction in an $S = 1$ two-leg Heisenberg spin ladder

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.

cond-mat.str-el↗
arXiv2021

Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons with a Flat Band

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.

cond-mat.quant-gas↗
arXiv2021

Generating Function for Tensor Network Diagrammatic Summation

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by computing variational excited states and dynamical structure factor of a quantum spin chain, and further investigating entanglement properties of excited states. Extensions to infinite size systems and higher dimension are outlined.

cond-mat.str-el↗
arXiv2021

Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction

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.

cond-mat.str-el↗
arXiv2021

DSQSS: Discrete Space Quantum Systems Solver

The Discrete Space Quantum Systems Solver (DSQSS) is a program package for solving quantum many-body problems defined on lattices. The DSQSS is based on the quantum Monte Carlo method in Feynman's path integral representation and covers a broad range of problems using flexible input files that define arbitrary unit cells in arbitrary dimensions and arbitrary matrix elements representing the interactions among an arbitrary number of degrees of freedom. Finite temperature calculations of quantum spin and the Bose- Hubbard models can be performed by specifying parameters such as the number of dimensions, the lattice size, coupling constants, and temperature. The present paper details the use of DSQSS and presents a number of applications thereof.

cond-mat.str-el↗
arXiv2021

Scaling dimensions from linearized tensor renormalization group transformations

We show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain scaling dimensions. The tensor RG methods have had a great success in producing accurate free energy compared with the conventional real-space RG schemes. However, the above-mentioned canonical procedure has not been implemented for general tensor-network-based RG schemes. We extend the success of the tensor methods further to extraction of scaling dimensions through the canonical RG prescription, without explicitly using the conformal field theory. This approach is benchmarked in the context of the Ising models in 1D and 2D. Based on a pure RG argument, the proposed method has potential applications to 3D systems, where the existing bread-and-butter method is inapplicable.

cond-mat.stat-mech↗
arXiv2020

Global optimization of tensor renormalization group using the corner transfer matrix

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.

cond-mat.stat-mech↗
arXiv2020

Continuous phase transition between Neel and valence bond solid phases in a J-Q-like spin ladder system

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 $β, η,$ and, $ν$ 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.

cond-mat.str-el↗
arXiv2020

Thermal Hall Effects of Spins and Phonons in Kagome Antiferromagnet Cd-Kapellasite

We have investigated the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field suppression effect on the longitudinal thermal conductivity k_xx sets in below ~25 K, suggesting a large spin contribution k_xx^sp in k_xx. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity k_xy shows a significant dependence on the sample's scattering time. On the other hand, the temperature dependence of k_xy is similar in all Cd-K samples; k_xy shows a peak at almost the same temperature of the peak of the phonon thermal conductivity k_xy^ph which is estimated by k_xx at 15 T. These results indicate the presence of a dominant phonon thermal Hall k_xy^ph at 15 T. In addition to k_xy^ph, we find that the field dependence of k_xy at low fields turns out to be non-linear at low temperatures, concomitantly with the appearance of the field suppression of k_xx, indicating the presence of a spin thermal Hall k_xy^sp at low fields. Remarkably, by assembling the k_xx dependene of k_xy^sp data of other kagome antiferromagnets, we find that, whereas k_xy^sp stays a constant in the low-k_xx region, k_xy^sp starts to increase as k_xx does in the high-k_xx region. This k_xx dependence of k_xy^sp indicates the presence of both intrinsic and extrinsic mechanisms in the spin thermal Hall effect in kagome antiferromagnets. Furthermore, both k_xy^ph and k_xy^sp disappear in the antiferromagnetic ordered phase at low fields, showing that phonons alone do not exhibit the thermal Hall effect. A high field above ~7 T induces k_xy^ph, concomitantly with a field-induced increase of k_xx and the specific heat, suggesting a coupling of the phonons to the field-induced spin excitations as the origin of k_xy^ph.

cond-mat.str-el↗