arXiv subjects

Tomotoshi Nishino

Publications and source records attributed to Tomotoshi Nishino.

At least 37 records · Page 2Linked to original sources

arXiv2017

Critical behavior of the two-dimensional icosahedron model

In the context of a discrete analogue of the classical Heisenberg model, we investigate critical behavior of the icosahedron model, where the interaction energy is defined as the inner product of neighboring vector spins of unit length pointing to vertices of the icosahedron. Effective correlation length and magnetization of the model are calculated by means of the corner-transfer matrix renormalization group (CTMRG) method. Scaling analysis with respect to the cutoff dimension $m$ in CTMRG reveals the second-order phase transition characterized by the exponents $ν= 1.62\pm0.02$ and $β= 0.12\pm0.01$. We also extract the central charge from the classical analogue of the entanglement entropy as $c = 1.90\pm0.02$, which cannot be explained by the minimal series of conformal field theory.

cond-mat.stat-mech↗

arXiv2016

Phase transition of the six-state clock model observed from the entanglement entropy

The Berezinskii-Kosterlitz-Thouless (BKT) transitions of the six-state clock model on the square lattice are investigated by means of the corner-transfer matrix renormalization group method. The classical analogue of the entanglement entropy $S( L, T )$ is calculated for $L$ by $L$ square system up to $L = 129$, as a function of temperature $T$. The entropy has a peak at $T = T^{*}_{~}( L )$, where the temperature depends on both $L$ and boundary conditions. Applying the finite-size scaling to $T^{*}_{~}( L )$ and assuming the presence of BKT transitions, the transition temperature is estimated to be $T_1^{~} = 0.70$ and $T_2^{~} = 0.88$. The obtained results agree with previous analyses. It should be noted that no thermodynamic function is used in this study.

cond-mat.stat-mech↗

arXiv2016

Phase diagram of truncated tetrahedral model

Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analogue of the entanglement entropy, which is numerically calculated by the corner transfer matrix renormalization group method. The obtained phase diagram consists of four different phases, which are separated by five transition lines. In the parameter region, where the octahedral anisotropy is dominant, a weak first-order phase transition is observed.

cond-mat.stat-mech↗

arXiv2015

Phase Transition of the Ising Model on Fractal Lattice

Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of four. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from that of the square-lattice Ising model. An exponential decay is observed in the density matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.

cond-mat.stat-mech↗

arXiv2014

Mean-field universality class induced by weak hyperbolic curvatures

Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the triangular lattice, where the typical distance between the nearest exceptional sites is proportional to an integer parameter $n$. Thus, the corresponding curvature is asymptotically proportional to $- n^{-2}_{~}$. Spontaneous magnetization and specific heat are calculated by means of the corner transfer matrix renormalization group method. For all the finite $n$ cases, we observe the mean-field-like phase transition. It is confirmed that the entanglement entropy at the transition temperature is linear in $(c / 6) \ln n$, where $c = 1 / 2$ is the central charge of the Ising model. The fact agrees with the presence of the typical length scale $n$ being proportional to the curvature radius.

cond-mat.stat-mech↗

arXiv2014

Doubling of Entanglement Spectrum in Tensor Renormalization Group

We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by `doubling' of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D = 64$, where $D$ is the cut-off dimension of tensors. At the critical point, we also find that a non-trivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.

cond-mat.stat-mech↗

arXiv2012

Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices

The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner transfer matrix renormalization group method using a recursive construction of asymmetric transfer matrices. Studying the phase transition, the mean-field universality is captured by means of a precise analysis of thermodynamic functions. The correlation functions and the density matrix spectra always decay exponentially even at the transition point, whereas power law behavior characterizes criticality on the Euclidean flat geometry. We confirm the absence of a finite correlation length in the limit of infinite negative Gaussian curvature.

cond-mat.stat-mech↗

arXiv2011

Connecting distant ends of one-dimensional critical systems by a sine-square deformation

We study the one-dimensional quantum critical spin systems with the sine-square deformation, in which the energy scale in the Hamiltonian at the position $x$ is modified by the function $f_x = \sin^2\left[π{L}(x-1/2)]$, where $L$ is the length of the system. By investigating the entanglement entropy, spin correlation functions, and wave-function overlap, we show that the sine-square deformation changes the topology of the geometrical connection of the ground state drastically; Although the system apparently has open edges, the sine-square deformation links those ends and realizes the periodic ground state at the level of wave function. Our results propose a new method to control the topology of quantum states by energy-scale deformation.

cond-mat.stat-mech↗

arXiv2011

Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation in Excitation Energy -

We investigate excitation energies of hyperbolically deformed S = 1 spin chains, which are specified by the local energy scale f_j^{~} = \cosh j λ, where j is the lattice index and λis the deformation parameter. The elementary excitation is well described by a quasiparticle hopping model, which is also expressed in the form of hyperbolic deformation. It is possible to estimate the excitation gap Δin the uniform limit λ\rightarrow 0, by means of a finite size scaling with respect to the system size N and the deformation parameter λ.

cond-mat.str-el↗

arXiv2010

Spherical Deformation for One-dimensional Quantum Systems

System-size dependence of the ground-state energy E^N is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as E^N / N - \lim_{N \to \infty} E^N / N, is of the order of 1 / N^2 when the reduction factor of the interaction is expressed by a sinusoidal function. We discuss the origin of this fast convergence from the view point of the spherical geometry.

cond-mat.str-el↗

arXiv2010

Scale free property and edge state of Wilson's numerical renormalization group

We discuss the scale-free property of Wilson's numerical renormalization group(NRG) for the Kondo impurity problem. The single-particle state of the effective Hamiltonian with a cutoff $Λ$ is described by the wavepacket basis having the scale free property; The energy scale of the system can be controlled by the lattice translation of the wavepacket basis with no reference of rescaling of the lattice space. We also analyze the role of the Kondo interaction in the context of wavepacket basis and then discuss the scaling and renormalization of the Kondo coupling. In addition, we clarify the role of the edge state in the lowest energy scale of Wilson NRG.

cond-mat.stat-mech↗

arXiv2010

Scaling Relation for Excitation Energy Under Hyperbolic Deformation

We introduce a one-parameter deformation for one-dimensional (1D) quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the j-th site. Corresponding to a 2D classical system, the deformation does not strongly modify the ground state. In this situation, the effective Hamiltonian of the quantum system shows that the quasi particle is weakly bounded around the center of the system. By analyzing this binding effect, we derive scaling relations for the mean-square width of confinement, the energy correction with respect to the excitation gap Δ, and the deformation parameter $λ$. This finite-size scaling allows us to investigate excitation gap of 1D non-deformed bulk quantum systems.

cond-mat.other↗

arXiv2010

Transverse Field Ising Model Under Hyperbolic Deformation

Ground state of the one-dimensional transverse field Ising model is investigated under the hyperbolic deformation, where the energy scale of j-th bond is proportional to the function \cosh ( j λ) that contains a parameter λ. Although the Hamiltonian is position dependent, the ground state is nearly uniform and finitely correlated. We observe the energy cross over between the ordered and disordered state with respect to the transverse field. The model shows first order phase transition, and the discontinuities in the magnetization and entanglement entropy at the transition point detect the Ising universality.

cond-mat.stat-mech↗

arXiv2010

Phase Transition of the Ising model on a Hyperbolic Lattice

The matrix product structure is considered on a regular lattice in the hyperbolic plane. The phase transition of the Ising model is observed on the hyperbolic $(5, 4)$ lattice by means of the corner-transfer-matrix renormalization group (CTMRG) method. Calculated correlation length is always finite even at the transition temperature, where mean-field like behavior is observed. The entanglement entropy is also always finite.

cond-mat.stat-mech↗

arXiv2009

A Classical Background for the Wave Function Prediction in the Infinite System DMRG Method

We report a physical background of the wave function prediction in the infinite system density matrix renormalization group (DMRG) method, from the view point of two-dimensional vertex model, a typical lattice model in statistical mechanics. Singular value decomposition applied to rectangular corner transfer matrices naturally draws matrix product representation for the maximal eigenvector of the row-to-row transfer matrix. The wave function prediction can be expressed as the insertion of an approximate half-column transfer matrix. This insertion process is in accordance with the scheme proposed by McCulloch recently.

cond-mat.stat-mech↗

arXiv2009

Gap Estimation by means of Hyperbolic Deformation

We present a way of numerical gap estimation applicable for one-dimensional infinite uniform quantum systems. Using the density matrix renormalization group method for a non-uniform Hamiltonian, which has deformed interaction strength of $j$-th bond proportional to $\cosh λj$, the uniform Hamiltonian is analyzed as a limit of $λ\to 0$. As a consequence of the deformation, an excited quasi-particle is weakly bounded around the center of the system, and kept away from the system boundary. Therefore, insensitivity of an estimated excitation gap of the deformed system to the boundary allows us to have the bulk excitation gap $Δ(λ)$, and shift in $Δ(λ)$ from $Δ(0)$ is nearly linear in $λ$ when $λ\ll 1$. Efficiency of this estimation is demonstrated through application to the S=1 antiferromagnetic Heisenberg chain. Combining the above estimation and another one obtained from the technique of convergence acceleration for finite-size gaps estimated by numerical diagonalizations, we conclude that the Haldane gap is in $[0.41047905,~0.41047931]$.

cond-mat.stat-mech↗

arXiv2008

Hyperbolic Deformation on Quantum Lattice Hamiltonians

A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic $1 + 1$-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to $\cosh j λ$, where $j$ is the lattice index and where $λ\ge 0$ is a deformation parameter. In the limit $λ\to 0$ the Hamiltonians become uniform. Spacial translation of the deformed Hamiltonians is induced by the corner Hamiltonians. As a simple example, we investigate the ground state of the deformed $S = 1/2$ Heisenberg spin chain by use of the density matrix renormalization group (DMRG) method. It is shown that the ground state is dimerized when $λ$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $λ$.

quant-ph↗

arXiv2008

Two-Site shift Product Wave Function Renormalization Group Method Applied to Quantum Systems

We report a way of wave function estimation for the density matrix renormalization group (DMRG) method applied to quantum systems, which has 2-site modulation, when the system size extension is necessary in both the finite and the infinite algorithms. The estimation is performed by renormalization group (RG) transformation applied to the ground state wave function, which is represented as the matrix product. This RG scheme is known as the product wave function renormalization group (PWFRG) method. In order to treat the 2-site modulation, the operation of the RG transformation is shifted by amount of 2 lattice sites. It turns out that this 2-site shift algorithm provides better wave function estimation in the thermodynamic limit, compared with the previously known PWFRG algorithm.

quant-ph↗