arXiv subjects

Tomotoshi Nishino

Publications and source records attributed to Tomotoshi Nishino.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic Field Induced by Straight Currents on the Hyperboloid

We consider the magnetic field induced by the steady or the quasi-steady electric currents that flow along the straight wires, which are equidistantly arranged on the hyperboloid. The spatial distribution of the magnetic field and the force acting on each wire are calculated. The continuum limit, where the wires are densely aligned, is also considered. We discuss the application of the hyperbolic current configuration to the generation of high magnetic fields.

physics.ed-ph↗

arXiv2025

Visualization of Entanglement Geometry by Structural Optimization of Tree Tensor Network

In tensor-network analysis of quantum many-body systems, it is of crucial importance to employ a tensor network with a spatial structure suitable for representing the state of interest. In the previous work [Hikihara et al., Phys. Rev. Research 5, 013031 (2023)], we proposed a structural optimization algorithm for tree-tensor networks. In this paper, we apply the algorithm to the Rainbow-chain model, which has a product state of singlet pairs between spins separated by various distances as an approximate ground state. We then demonstrate that the algorithm can successfully visualize the spatial pattern of spin-singlet pairs in the ground state.

cond-mat.stat-mech↗

arXiv2025

Improving accuracy of tree-tensor network approach by optimization of network structure

Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state crucially depends on the spatial structure of the network. In the previous work [Hikihara et al., Phys. Rev. Res. 5, 013031 (2023)], we proposed an algorithm based on tree tensor networks (TTNs) that automatically optimizes the structure of TTN according to the spatial profile of entanglement in the state of interest. In this paper, we apply the algorithm to the random XY-exchange model under random magnetic fields and the Richardson model in order to analyze how the performance of the algorithm depends on the detailed updating schemes of the structural optimization. We then find that for the random XY model, on the one hand, the algorithm achieves improved accuracy, and the stochastic algorithm, which selects the local network structure probabilistically, is notably effective. For the Richardson model, on the other hand, the resulting numerical accuracy subtly depends on the initial TTN and the updating schemes. In particular, the algorithm without the stochastic updating scheme certainly improves the accuracy, while the one with the stochastic updates results in poor accuracy due to the effect of randomizing the network structure at the early stage of the calculation. These results indicate that the algorithm successfully improves the accuracy of the numerical calculations for quantum many-body states, while it is essential to appropriately choose the updating scheme as well as the initial TTN structure, depending on the systems treated.

cond-mat.stat-mech↗

arXiv2025

Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice

The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension $d_H = \ln32 / \ln4 = 2.5$ is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine the critical temperature $T_c \approx 2.65231$ and the critical exponents for magnetization $β\approx 0.059$ and field response $δ\approx 35$. Unlike a previously studied 2D fractal with $d_H \approx 1.792$, the specific heat for this 3D fractal exhibits a divergent singularity at $T_c$. The results are compared with those for regular lattices and other fractal structures to elucidate the role of dimensionality in critical phenomena.

cond-mat.stat-mech↗

arXiv2025

Tensor network calculation of boundary and corner magnetization

The Corner Transfer Matrix Renormalization Group (CTMRG) algorithm is modified to measure the magnetization at the boundary of the system, including the corners of the square-shaped lattice. Using automatic differentiation, we calculate the magnetization's first derivative, allowing us to determine the boundary critical exponent $β$ accurately.

cond-mat.stat-mech↗

arXiv2025

Quantum Potts Models on the Sierpiński Pyramid

Phase transition of the two- and three-state quantum Potts models on the Sierpiński pyramid are studied by means of a tensor network framework, the higher-order tensor renormalization group method. Critical values of the transverse magnetic field and the magnetic exponent $β$ are evaluated. Despite the fact that the Hausdorff dimension of the Sierpiński pyramid is exactly two $( = \log_2^{~} 4)$, the obtained critical properties show that the effective dimension is lower than two.

cond-mat.stat-mech↗

arXiv2024

Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model

We analyze boundary spin correlation functions of the hyperbolic-lattice Ising model from the holographic point of view. Using the corner-transfer-matrix renormalization group (CTMRG) method, we demonstrate that the boundary correlation function exhibits power-law decay with quasi-periodic oscillation, while the bulk correlation function always decays exponentially. On the basis of the geometric relation between the bulk correlation path and distance along the outer edge boundary, we find that scaling dimensions for the boundary correlation function can be well explained by the combination of the bulk correlation length and background curvatures inherent to the hyperbolic lattice. We also investigate the cutoff effect of the bond dimension in CTMRG, revealing that the long-distance behavior of the boundary spin correlation is accurately described even with a small bond dimension. In contrast, the sort-distance behavior rapidly loses its accuracy.

cond-mat.stat-mech↗

arXiv2024

Ferromagnetic Ising model on the hierarchical pentagon lattice

Thermodynamic properties of the ferromagnetic Ising model on the hierarchical pentagon lattice is studied by means of the tensor network methods. The lattice consists of pentagons, where 3 or 4 of them meet at each vertex. Correlation functions on the surface of the system up to n = 10 layers are evaluated by means of the time evolving block decimation (TEBD) method, and the power low decay is observed in the high temperature region. The recursive structure of the lattice enables complemental numerical study for larger systems, by means of a variant of the corner transfer matrix renormalization group (CTMRG) method. Calculated spin expectation value shows that there is a mean-field type order-disorder transition at T1 = 1.58 on the surface of the system. On the other hand, the bulk part exhibits the transition at T2 = 2.269. Consistency of these calculated results is examined.

cond-mat.stat-mech↗

arXiv2023

Measurements of magnetization on the Sierpiński carpet

Phase transition of the classical Ising model on the Sierpiński carpet, which has the fractal dimension $\log_3^{~} 8 \approx 1.8927$, is studied by an adapted variant of the higher-order tensor renormalization group method. The second-order phase transition is observed at the critical temperature $T_{\rm c}^{~} \approx 1.478$. Position dependence of local functions is studied through impurity tensors inserted at different locations on the fractal lattice. The critical exponent $β$ associated with the local magnetization varies by two orders of magnitude, depending on lattice locations, whereas $T_{\rm c}^{~}$ is not affected. Furthermore, we employ automatic differentiation to accurately and efficiently compute the average spontaneous magnetization per site as a first derivative of free energy with respect to the external field, yielding the global critical exponent of $β\approx 0.135$.

cond-mat.stat-mech↗

arXiv2023

Entanglement bipartitioning and tree tensor networks

We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of spin-cluster nodes so as to minimize the mutual information or the maximum loss of the entanglement entropy associated with the branch to be bipartitioned. We demonstrate that entanglement bipartitioning of up to 16 sites gives rise to nontrivial tree network structures for $S=1/2$ Heisenberg models in one and two dimensions. The resulting TTNs enable us to obtain better variational energies, compared with standard TTNs such as uniform matrix product state and perfect-binary-tree tensor network.

quant-ph↗

arXiv2022

Automatic structural optimization of tree tensor networks

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground-state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.

cond-mat.stat-mech↗

arXiv2022

Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a unified description of a series of developments in the TN from the statistical mechanics side. In particular, we begin with the variational principle for the transfer matrix of the 2D Ising model, which naturally leads us to the matrix product state (MPS) and the corner transfer matrix (CTM). We then explain how the CTM can be evolved to such MPS-based approaches as density matrix renormalization group (DMRG) and infinite time-evolved block decimation. We also elucidate that the finite-size DMRG played an intrinsic role for incorporating various quantum information concepts in subsequent developments in the TN. After surveying higher-dimensional generalizations like tensor product states or projected entangled pair states, we describe tensor renormalization groups (TRGs), which are a fusion of TNs and Kadanoff-Wilson type real-space renormalization groups, focusing on their fixed point structures. We then discuss how the difficulty in TRGs for critical systems can be overcome in the tensor network renormalization and the multi-scale entanglement renormalization ansatz.

cond-mat.stat-mech↗

arXiv2022

Energy Scale Deformation on Regular Polyhedra

A variant of energy scale deformation is considered for the S = 1/2 antiferromagnetic Heisenberg model on polyhedra. The deformation is induced by the perturbations to the uniform Hamiltonian, whose coefficients are determined by the bond coordinates. On the tetrahedral, octahedral, and cubic clusters, the perturbative terms do not affect the ground state of the uniform Hamiltonian when they are sufficiently small. On the other hand, for the icosahedral and dodecahedral clusters, it is numerically confirmed that the ground state of the uniform Hamiltonian is almost insensitive to the perturbations unless they lead to a discontinuous change in the ground state. The obtained results suggest the existence of a generalization of sine-square deformation in higher dimensions.

cond-mat.str-el↗

arXiv2020

Phase transition of the four-dimensional cross-polytope model

Thermodynamic properties of the four-dimensional cross-polytope model, the 16-cell model, which is an example of higher dimensional generalizations of the octahedron model, are studied on the square lattice. By means of the corner transfer matrix renormalization group (CTMRG) method, presence of the first-order phase transition is confirmed. The latent heat is estimated to be $L_4^{~} = 0.3172$, which is larger than that of the octahedron model $L_3^{~} = 0.0516$. The result suggests that the latent heat increases with the internal dimension $n$ when the higher-dimensional series of the cross-polytope models is considered.

cond-mat.stat-mech↗

arXiv2020

Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model

We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analogue of the classical Heisenberg model, which has continuous $O(3)$ symmetry. In order to treat the large on-site degree of freedom $q = 20$, we develop a massively parallelized numerical algorithm for the corner transfer matrix renormalization group method, incorporating EigenExa, the high-performance parallelized eigensolver. The scaling analysis with respect to the cutoff dimension reveals that there is a second-order phase transition at $T^{~}_{\rm c}=0.4398(8)$ with the critical exponents $ν=2.88(8)$ and $β=0.21(1)$. The central charge of the system is estimated as $c=1.99(6)$.

cond-mat.stat-mech↗

arXiv2020

Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the $c=1$ boundary conformal field theory associated with the effective $Z_6$ dual sine-Gordon model.

cond-mat.stat-mech↗

arXiv2020

Tensor Networks: Phase transition phenomena on hyperbolic and fractal geometries

One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several numerical simulation methods have been proposed in recent years. Amongst all of them, the Tensor Network algorithms have become increasingly popular in recent years, especially for their adaptability to simulate strongly correlated systems. The current work focuses on the generalization of such Tensor-Network-based algorithms, which are sufficiently robust to describe critical phenomena and phase transitions of multistate spin Hamiltonians in the thermodynamic limit. We have chosen two algorithms: the Corner Transfer Matrix Renormalization Group and the Higher-Order Tensor Renormalization Group. This work, based on tensor-network analysis, opens doors for the understanding of phase transition and entanglement of the interacting systems on the non-Euclidean geometries. We focus on three main topics: A new thermodynamic model of social influence, free energy is analyzed to classify the phase transitions on an infinite set of the negatively curved geometries where a relation between the free energy and the Gaussian radius of the curvature is conjectured, a unique tensor-based algorithm is proposed to study the phase transition on fractal structures.

cond-mat.stat-mech↗

arXiv2018

Tensor-network study of quantum phase transition on Sierpiński fractal

The transverse-field Ising model on the Sierpiński fractal, which is characterized by the fractal dimension $\log_2^{~} 3 \approx 1.585$, is studied by a tensor-network method, the Higher-Order Tensor Renormalization Group. We analyze the ground-state energy and the spontaneous magnetization in the thermodynamic limit. The system exhibits the second-order phase transition at the critical transverse field $h_{\rm c}^{~} = 1.865$. The critical exponents $β\approx 0.198$ and $δ\approx 8.7$ are obtained. Complementary to the tensor-network method, we make use of the real-space renormalization group and improved mean-field approximations for comparison.

cond-mat.stat-mech↗