arXiv subjects

Naoki Kawashima

Publications and source records attributed to Naoki Kawashima.

At least 19 recordsLinked to original sources

arXiv2026

Gauge-constrained Spinon Complexes Near Deconfined Quantum Criticality

Quantum magnets provide a microscopic platform for studying confinement and gauge-constrained structures mediated by emergent gauge fields. We investigate confined spinon complexes in the columnar valence-bond-solid (VBS) phase near deconfined quantum criticality using pinned-spin defects and quantum Monte Carlo simulations. The pinned spins act as static spinon sources with controlled positions, spin projections, and VBS vorticities, enabling measurement of defect energies and direct real-space visualization of the associated VBS domain-wall strings. For matched spinon-antispinon sources, the excitation energy saturates beyond a characteristic separation as one extended dipole reorganizes into two shorter neutral dipoles, providing energetic and real-space evidence of string breaking. We further show that domain-wall connectivity is governed by lattice-scale VBS phase offsets in addition to vorticity and spin-projection neutrality. Compatible multi-pin patterns generate connected four-spinon complexes and extended domain-wall networks that retain their global connectivity under local distortions. These results establish pinned-spin defects as a controlled tool for assembling and resolving multi-spinon structures and their confining strings in a VBS phase.

cond-mat.str-el↗

arXiv2026

Universal Information-Theoretic Structure of the Quasi-Stationary Domany--Kinzel Automaton

We characterize the quasi-stationary distribution (QSD) of the bond directed-percolation line of the Domany--Kinzel automaton using a matrix-product-state representation of the probability distribution, obtained by projecting out the absorbing state and iterating the transfer matrix. Unlike moment- or sampling-based methods, this yields the full conditional distribution and direct access to information-theoretic diagnostics. The spatial structure of the QSD changes sharply across the transition: the active phase is bulk-like with finite density, whereas in the inactive phase the surviving activity collapses into a single flock -- the smallest interval containing all active sites -- occupying a vanishing fraction of the chain. Throughout the inactive phase the bipartite mutual information of the QSD equals the entropy of a single binary choice -- whether the flock lies to the left or right of the cut -- so the surviving clusters together encode just one bit of positional information, corresponding to a single effective cluster.

cond-mat.stat-mech↗

arXiv2025

Tensor Renormalization Group Calculations of Partition-Function Ratios

The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal field theory (CFT) through the modular-invariant partition functions on a torus. We perform numerical calculations using the bond-weighted tensor renormalization group for three two-dimensional models belonging to different universality classes: the Ising model, the three-state Potts model, and the four-state Potts model. The partition-function ratios obey the same finite-size scaling form as the Binder parameter, and their critical values agree well with the universal values predicted by CFT. In the four-state Potts model, we observe logarithmic corrections in the system-size dependence of these ratios.

cond-mat.stat-mech↗

arXiv2025

Lattice-reflection symmetry in tensor-network renormalization group with entanglement filtering in two and three dimensions

Tensor-network renormalization group (TNRG) is an efficient real-space renormalization group method for studying the criticality in both classical and quantum lattice systems. Exploiting symmetries of a system in a TNRG algorithm can simplify the implementation of the algorithm and can help produce correct tensor RG flows. Although a general framework for considering a global on-site symmetry has been established, it is still unclear how to incorporate a lattice symmetry in TNRG. As a first step for lattice symmetries, we propose a method to incorporate the lattice-reflection symmetry in the context of a TNRG with entanglement filtering in both two and three dimensions (2D and 3D). To achieve this, we write down a general definition of lattice-reflection symmetry in tensor-network language. Then, we introduce a transposition trick for exploiting and imposing the lattice-reflection symmetry in two basic TNRG operations: projective truncations and entanglement filtering. Using the transposition trick, the detailed algorithms of the TNRG map in both 2D and 3D are laid out, where the lattice-reflection symmetry is preserved and imposed. Finally, we demonstrate how to construct the linearization of the TNRG maps in a given lattice-reflection sector, with the help of which it becomes possible to extract scaling dimensions in each sector separately. Our work paves the way for understanding the lattice-rotation symmetry in TNRG.

cond-mat.stat-mech↗

arXiv2025

Variational boundary based tensor network renormalization group

We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment for the entire system. Based on this optimized environment, we construct renormalization projectors that significantly enhance accuracy. By leveraging the canonical form of tensors, our algorithm maintains the same computational complexity as the original tensor renormalization group (TRG) method, yet achieves higher accuracy than existing approaches that do not incorporate entanglement filtering. Our work offers a practical pathway for extending TRG methods to higher dimensions while keeping computational costs manageable.

cond-mat.stat-mech↗

arXiv2025

Superfluid dome in the spatially modulated two-dimensional XY model

In strongly correlated electron systems, superconductivity and charge density waves often coexist in close proximity, suggesting a deeper relationship between these competing phases. Recent research indicates that these orders can intertwine, with the superconducting order parameter coupling to modulations in the electronic density. To elucidate this interplay, we study a two-dimensional XY model with a periodic modulation of the coupling strength in one spatial direction. Using a combination of tensor network methods and Monte Carlo simulations, we reveal a non-monotonic, dome-like dependence of $T_c$ on the modulation wavelength, with the peak $T_c$ shifting to longer wavelengths as the modulation strength grows. The origin of this phenomenon is traced back to an effective pinning of vortices in the valleys of the modulation, confirmed by a comparison to modulated $q$-state clock models. These findings shed new light on the phase behavior of intertwined superconducting and charge-ordered states, offering a deeper understanding of their complex interactions.

cond-mat.supr-con↗

arXiv2025

Project For Advancement of Software Usability in Materials Science

The Institute for Solid State Physics (ISSP) at The University of Tokyo has been carrying out a software development project named ``the Project for Advancement of Software Usability in Materials Science (PASUMS)". Since the launch of PASUMS, various open-source software programs have been developed/advanced, including ab initio calculations, effective model solvers, and software for machine learning. We also focus on activities that make the software easier to use, such as developing comprehensive computing tools that enable efficient use of supercomputers and interoperability between different software programs. We hope to contribute broadly to developing the computational materials science community through these activities.

cs.SE↗

arXiv2025

Plastic tensor networks for interpretable generative modeling

A structural optimization scheme for a single-layer nonnegative adaptive tensor tree (NATT) that models a target probability distribution is proposed as an alternative paradigm for generative modeling. The NATT scheme, by construction, automatically searches for a tree structure that best fits a given discrete dataset whose features serve as inputs, and has the advantage that it is interpretable as a probabilistic graphical model. We consider the NATT scheme and a recently proposed Born machine adaptive tensor tree (BMATT) optimization scheme and demonstrate their effectiveness on a variety of generative modeling tasks where the objective is to infer the hidden structure of a provided dataset. Our results show that in terms of minimizing the negative log-likelihood, the single-layer scheme has model performance comparable to the Born machine scheme, though not better. The tasks include deducing the structure of binary bitwise operations, learning the internal structure of random Bayesian networks given only visible sites, and a real-world example related to hierarchical clustering where a cladogram is constructed from mitochondrial DNA sequences. In doing so, we also show the importance of the choice of network topology and the versatility of a least-mutual information criterion in selecting a candidate structure for a tensor tree, as well as discuss aspects of these tensor tree generative models including their information content and interpretability.

cs.LG↗

arXiv2025

TeNeS-v2: Enhancement for Real-Time and Finite Temperature Simulations of Quantum Many-Body Systems

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.

cond-mat.str-el↗

arXiv2024

Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches

We investigate the finite-temperature phase diagram of the classical $J_1$-$J_2$ XY model on a square lattice using a tensor network approach designed for frustrated spin systems. This model, characterized by competing nearest-neighbor and next-to-nearest-neighbor interactions, exhibits a complex interplay between $U(1)$ and $Z_2$ symmetries. Our study reveals an emergent intermediate phase around $J_2/J_1 \sim 0.505$, which is characterized by a $Z_2$ long-range stripe order without phase coherence in the XY spins. The intermediate phase features two well-separated phase transitions: a higher-temperature Ising transition and a lower-temperature Berezinskii-Kosterlitz-Thouless transition. The relative separation between these transitions is significantly larger than previously reported, enabling a clearer investigation of their distinct thermodynamic properties. For $0.5<J_2/J_1 < 0.501$, two transitions merge into a single first-order phase transition, a phenomenon that cannot be explained solely by mapping to the Ising-XY model. As $J_2/J_1 \to \infty$, the transition evolves continuously into the BKT universality class. These findings advance the understanding of the mechanisms driving phase transitions in frustrated spin systems and suggest potential experimental realizations in platforms such as ultracold atoms, Josephson junction arrays, and optical lattices.

cond-mat.str-el↗

arXiv2024

Three-dimensional real space renormalization group with well-controlled approximations

We make Kadanoff's block idea into a reliable three-dimensional (3D) real space renormalization group (RG) method. Kadanoff's idea, expressed in spin representation, offers a qualitative intuition for clarifying scaling behavior in criticality, but has difficulty as a quantitative tool due to uncontrolled approximations. A tensor-network reformulation equips the block idea with a measure of RG errors. In 3D, we propose an entanglement filtering scheme to enhance such a block-tensor map, with the lattice reflection symmetry exploited. When the proposed RG is applied to the cubic-lattice Ising model, the RG errors are reduced to about 2% by retaining more couplings. The estimated scaling dimensions of the two relevant fields have errors 0.4% and 0.1% in the best case, compared with the accepted values. The proposed RG is promising as a systematically-improvable real space RG method in 3D. The unique feature of our method is its ability to numerically obtain a 3D critical fixed point in a high-dimensional tensor space. A fixed-point tensor contains much more information than a handful of observables estimated in conventional techniques for analyzing critical systems.

cond-mat.stat-mech↗

arXiv2024

Multi-impurity method for the bond-weighted tensor renormalization group

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 five-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.

cond-mat.stat-mech↗

arXiv2024

Tensor tree learns hidden relational structures in data to construct generative models

Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S&P500. In (i) and (ii), the strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and in (iv), a structure corresponding to the eleven sectors emerged.

cs.LG↗

arXiv2024

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge upon the quantum order by disorder effect of the $S=1/2$ system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of sub-extensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Adopting the the real space perturbation theory, our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When $J$ becomes larger, we adopt the infinite projected entangled-pair state~(iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for the two-dimensional quantum simulators.

cond-mat.quant-gas↗

arXiv2024

Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice

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.

cond-mat.stat-mech↗

arXiv2024

Faithfulness of Real-Space Renormalization Group Maps

The behavior of $b=2$ real-space renormalization group (RSRG) maps like the majority rule and the decimation map was examined by numerically applying RSRG steps to critical $q=2,3,4$ Potts spin configurations. While the majority rule is generally believed to work well, a more thorough investigation of the action of the map has yet to be considered in the literature. When fixing the size of the renormalized lattice $L_g$ and allowing the source configuration size $L_0$ to vary, we observed that the RG flow of the spin and energy correlation under the majority rule map appear to converge to a nontrivial model-dependent curve. We denote this property as "faithfulness", because it implies that some information remains preserved by RSRG maps that fall under this class. Furthermore, we show that $b=2$ weighted majority-like RSRG maps acting on the $q=2$ Potts model can be divided into two categories, maps that behave like decimation and maps that behave like the majority rule.

cond-mat.stat-mech↗

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

Essential difference between 2D and 3D from the perspective of real-space renormalization group

We point out that area laws of quantum-information concepts indicate limitations of block transformations as well-behaved real-space renormalization group (RG) maps, which in turn guides the design of better RG schemes. Mutual-information area laws imply the difficulty of Kadanoff's block-spin method in two dimensions (2D) or higher due to the growth of short-scale correlations among the spins on the boundary of a block. A leap to the tensor-network RG, in hindsight, follows the guidance of mutual information and is efficient in 2D, thanks to its mixture of quantum and classical perspectives and the saturation of entanglement entropy in 2D. In three dimensions (3D), however, entanglement grows according to the area law, posing a threat to 3D block-tensor map as an apt RG transformation. As a numerical evidence, we show that estimations of 3D Ising critical exponents fail to improve by retaining more couplings. As a guidance to proceed, a tensor-network toy model is proposed to capture the 3D entanglement-entropy area law.

cond-mat.stat-mech↗