arXiv subjects

T. Nishino

Publications and source records attributed to T. Nishino.

At least 19 recordsLinked to original sources

arXiv2020

Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line

A classical analogue of the entanglement entropy is calculated on the system boundary of the two-dimensional Edwards-Anderson model, where the nearest-neighbor interaction is stochastically chosen from +J and -J. The boundary spin distribution is obtained by means of the time-evolving block decimation (TEBD) method, where the random ensemble is created from the successive multiplications of position-dependent transfer matrices, whose width is up to N = 300. The random average of the entanglement entropy is calculated on the Nishimori line, and it is confirmed that the entanglement entropy shows critical singularity at the Nishimori point. The central charge of the boundary state is estimated.

cond-mat.dis-nn↗

arXiv2015

Analysis of Cortical Morphometric Variability Using Labeled Cortical Distance Maps

Morphometric differences in the anatomy of cortical structures are associated with neuro-developmental and neuropsychiatric disorders. Such differences can be quantized and detected by a powerful tool called Labeled Cortical Distance Map (LCDM). The LCDM method pro-vides distances of labeled gray matter (GM) voxels from the GM/white matter (WM) surface for specific cortical structures (or tissues). Here we describe a method to analyze morphometric variability in the particular tissue using LCDM distances. To extract more of the information provided by LCDM distances, we perform pooling and censoring of LCDM distances. In particular, we employ Brown-Forsythe (BF) test of homogeneity of variance (HOV) on the LCDM distances. HOV analysis of pooled distances provides an overall analysis of morphometric variability of the LCDMs due to the disease in question, while the HOV analysis of censored distances suggests the location(s) of significant variation in these differences (i.e., at which distance from the GM/WM surface the morphometric variability starts to be significant). We also check for the influence of assumption violations on the HOV analysis of LCDM distances. In particular, we demonstrate that BF HOV test is robust to assumption violations such as the non-normality and within sample dependence of the residuals from the median for pooled and censored distances and are robust to data aggregation which occurs in analysis of censored distances. We illustrate the methodology on a real data example, namely, LCDM distances of GM voxels in ventral medial prefrontal cortices (VMPFCs) to see the effects of depression or being of high risk to depression on the morphometry of VMPFCs. The methodology used here is also valid for morphometric analysis of other cortical structures.

stat.AP↗

arXiv2015

Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

We present a modification of Matrix Product State time evolution to simulate the propagation of signal fronts on infinite one-dimensional systems. We restrict the calculation to a window moving along with a signal, which by the Lieb-Robinson bound is contained within a light cone. Signal fronts can be studied unperturbed and with high precision for much longer times than on finite systems. Entanglement inside the window is naturally small, greatly lowering computational effort. We investigate the time evolution of the transverse field Ising (TFI) model and of the S=1/2 XXZ antiferromagnet in their symmetry broken phases after several different local quantum quenches. In both models, we observe distinct magnetization plateaus at the signal front for very large times, resembling those previously observed for the particle density of tight binding (TB) fermions. We show that the normalized difference to the magnetization of the ground state exhibits similar scaling behaviour as the density of TB fermions. In the XXZ model there is an additional internal structure of the signal front due to pairing, and wider plateaus with tight binding scaling exponents for the normalized excess magnetization. We also observe parameter dependent interaction effects between individual plateaus, resulting in a slight spatial compression of the plateau widths. In the TFI model, we additionally find that for an initial Jordan-Wigner domain wall state, the complete time evolution of the normalized excess longitudinal magnetization agrees exactly with the particle density of TB fermions.

cond-mat.str-el↗

arXiv2013

Censoring Distances Based on Labeled Cortical Distance Maps in Cortical Morphometry

Shape differences are manifested in cortical structures due to neuropsychiatric disorders. Such differences can be measured by labeled cortical distance mapping (LCDM) which characterizes the morphometry of the laminar cortical mantle of cortical structures. LCDM data consist of signed distances of gray matter (GM) voxels with respect to GM/white matter (WM) surface. Volumes and descriptive measures (such as means and variances) for each subject and the pooled distances provide the morphometric differences between diagnostic groups, but they do not reveal all the morphometric information contained in LCDM distances. To extract more information from LCDM data, censoring of the distances is introduced. For censoring of LCDM distances, the range of LCDM distances is partitioned at a fixed increment size; and at each censoring step, and distances not exceeding the censoring distance are kept. Censored LCDM distances inherit the advantages of the pooled distances. Furthermore, the analysis of censored distances provides information about the location of morphometric differences which cannot be obtained from the pooled distances. However, at each step, the censored distances aggregate, which might confound the results. The influence of data aggregation is investigated with an extensive Monte Carlo simulation analysis and it is demonstrated that this influence is negligible. As an illustrative example, GM of ventral medial prefrontal cortices (VMPFCs) of subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy control (Ctrl) subjects are used. A significant reduction in laminar thickness of the VMPFC and perhaps shrinkage in MDD and HR subjects is observed when compared to Ctrl subjects. The methodology is also applicable to LCDM-based morphometric measures of other cortical structures affected by disease.

stat.AP↗

arXiv2011

Suppression of finite-size effects in one-dimensional correlated systems

We investigate the effect of a non-uniform deformation applied to one-dimensional (1D) quantum systems, where the local energy scale is proportional to $g_j = [\sin (j π/ N)]^m$ determined by a positive integer $m$, site index $1 \leq j \leq N-1$, and the system size N. This deformation introduces a smooth boundary to systems with open boundary conditions. When $m \geq 2$, the leading $1/N$ correction to the ground state energy per bond $e_0^{(N)}$ vanishes and one is left with a $1/N^2$ correction, the same as with periodic boundary conditions. In particular, when $m = 2$, the value of $e_0^{(N)}$ obtained from the deformed open-boundary system coincides with the uniform system with periodic boundary conditions. We confirm the fact numerically for correlated systems, such as the extended Hubbard model, in addition to 1D free-Fermion models.

cond-mat.str-el↗

arXiv2008

Tricritical point of J1-J2 Ising model on hyperbolic lattice

A ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains ferromagnetic nearest-neighbor interaction J_1 and the competing antiferromagnetic interaction J_2. A mean-field like second-order phase transition is observed when the ratio κ= J_2 / J_1 is less than 0.203. In the region 0.203 < κ< 1/4, the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field like.

cond-mat.stat-mech↗

arXiv2008

The Use of Labeled Cortical Distance Maps for Quantization and Analysis of Anatomical Morphometry of Brain Tissues

Anatomical shape differences in cortical structures in the brain can be associated with various neuropsychiatric and neuro-developmental diseases or disorders. Labeled Cortical Distance Map (LCDM), can be a powerful tool to quantize such morphometric differences. In this article, we investigate various issues regarding the analysis of LCDM distances in relation to morphometry. The length of the LCDM distance vector provides the number of voxels (approximately a multiple of volume (in mm^3)); median, mode, range, and variance of LCDM distances are all suggestive of size, thickness, and shape differences. However these measures provide a crude summary based on LCDM distances which may convey much more information about the tissue in question. To utilize more of this information, we pool (merge) the LCDM distances from subjects in the same group or condition. The statistical methodology we employ require normality and within and between sample independence. We demonstrate that the violation of these assumptions have mild influence on the tests. We specify the types of alternatives the parametric and nonparametric tests are more sensitive for. We also show that the pooled LCDM distances provide powerful results for group differences in distribution, left-right morphometric asymmetry of the tissues, and variation of LCDM distances. As an illustrative example, we use gray matter (GM) tissue of ventral medial prefrontal cortices (VMPFCs) from subjects with major depressive disorder, subjects at high risk, and control subjects. We find significant evidence that VMPFCs of subjects with depressive disorders are different in shape compared to those of normal subjects.

stat.CO↗

arXiv2004

Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by each according to the conditional probability with respect to its environment.

cond-mat.stat-mech↗

arXiv2004

Tensor Product Variational Formulation for Quantum Systems

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group method (DMRG) to infinite size 2D quantum systems.

cond-mat.stat-mech↗

arXiv2002

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.

cond-mat.stat-mech↗

arXiv2000

Self-Consistent Tensor Product Variational Approximation for 3D Classical Models

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is investigated through trial applications to the 3D Ising model and the 3D 3-state Potts model.

cond-mat.stat-mech↗

arXiv1999

Efficiency of symmetric targeting for finite-T DMRG

Two targeting schemes have been known for the density matrix renormalization group (DMRG) applied to non-Hermitian problems; one uses an asymmetric density matrix and the other uses symmetric density matrix. We compare the numerical efficiency of these two targeting schemes when they are used for the finite temperature DMRG.

cond-mat.stat-mech↗

arXiv1998

Fixed Point of the Finite System DMRG

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B**B. This is because the tensors are not improved directly. We overcome this problem by using the simpler block structure B*B for the final several sweeps in the finite iteration process. It is possible to increase the numerical precision of the finite system algorithm without increasing the computational effort.

cond-mat.stat-mech↗

arXiv1998

Spin, Charge and Quasiparticle Gaps in the One-Dimensional Kondo Lattice with f^2 Configuration

The ground state properties of the one-dimensional Kondo lattice with an f^2 configuration at each site are studied by the density matrix renormalization group method. At half-filling, competition between the Kondo exchange J and the antiferromagnetic intra f-shell exchange I leads to reduction of energy gaps for spin, quasi-particle and charge excitations. The attractive force among conduction electrons is induced by the competition and the bound state is formed. As J/I increases the f^2 singlet gives way to the Kondo singlet as the dominant local correlation. The remarkable change of the quasi-particle gap is driven by the change of the spin-1/2 excitation character from the itinerant one to the localized one. Possible metal-insulator transition is discussed which may occur as the ratio J/I is varied by reference to mean-field results in the f^2 lattice system and the two impurity Kondo system.

cond-mat.str-el↗

arXiv1997

One-dimensional Heisenberg antiferromagnet in which two S=1/2 and two S=1 spins are arranged alternatively

Ground-state and thermodynamic properties of the one-dimensional Heisenberg antiferromagnet in which two S=1/2 and two S=1 spins are arranged alternatively are studied by a quantum Monte Carlo method and by analytical estimates. It is found that the ground state of the system undergoes a second-order phase transition which accompanies the vanishing of the energy gap.

cond-mat.str-el↗

arXiv1997

Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains

We present a rotationally invariant matrix product method (MPM) of isotropic spin chains. This allows us to deal with a larger number of variational MPM parameters than those considered earlier by other authors. We also show the relation between the MPM and the DMRG method of White. In our approach the eigenstates of the density matrix associated with the MPM are used as variational parameters together with the standard MPM parameters. We compute the ground state energy density and the spin correlation length of the spin 1 Heisenberg chain.

cond-mat.str-el↗

arXiv1996

The Density Matrix Renormalization Group Method applied to Interaction Round a Face Hamiltonians

Given a Hamiltonian with a continuous symmetry one can generally factorize that symmetry and consider the dynamics on invariant Hilbert Spaces. In Statistical Mechanics this procedure is known as the vertex-IRF map, and in certain cases, like rotational invariant Hamiltonians, can be implemented via group theoretical techniques. Using this map we translate the DMRG method, which applies to 1d vertex Hamiltonians, into a formulation adequate to study IRF Hamiltonians. The advantage of the IRF formulation of the DMRG method ( we name it IRF-DMRG), is that the dimensions of the Hilbert Spaces involved in numerical computations are smaller than in the vertex-DMRG, since the degeneracy due to the symmetry has been eliminated. The IRF-DMRG admits a natural and geometric formulation in terms of the paths or string algebras used in Exactly Integrable Systems and Conformal Field Theory. We illustrate the IRF-DMRG method with the study of the SOS model which corresponds to the spin 1/2 Heisenberg chain and the RSOS models with Coxeter diagram of type A, which correspond to the quantum group invariant XXZ chain.

cond-mat.stat-mech↗

arXiv1996

Density Matrix and Renormalization for Classical Lattice Models

We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state energy. The variational principle is applied to two-dimensional (2D) classical lattice models, where the density matrix is expressed as a product of corner transfer matrices. (CTMs) DMRG related fields and future directions of DMRG are briefly discussed.

cond-mat.stat-mech↗