Yasuhiro Hieida

Two-Dimensional Tensor Product Variational Formulation

We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model.

MIDDLE-FIELD CUSP SINGULARITIES IN THE MAGNETIZATION PROCESS OF ONE-DIMENSIONAL QUANTUM ANTIFERROMAGNETS

We study the zero-temperature magnetization process (M-H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2 zig-zag spin ladder and the S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M-H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.

Magnetization process of a one-dimensional quantum antiferromagnet: The product-wave-function renormalization group approach☆

Abstract The product-wave-function renormalization group method, a new numerical renormalization group scheme proposed recently, is applied to one-dimensional quantum spin chains in a magnetic field. We find the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.

Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit.

We study the asymptotic behavior of the eigenvalue distribution of the corner transfer matrix (M(CTM)) and the density matrix (M(DM)) in the density-matrix renormalization group. We utilize the relationship M(DM)=M(4)(CTM), which holds for noncritical systems in the thermodynamic limit. We derive the exact and universal asymptotic form of the M(DM) eigenvalue distribution for a class of integrable models in the massive regime. For nonintegrable models, the universal asymptotic form is also verified by numerical renormalization group calculations.

Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile (one-point function). We show that, even with a small number of retained bases, the DMRG calculation is in excellent agreement with the exact solution obtained by the matrix-product-ansatz approach.

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.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.

Effects of Bottlenecks on Vehicle Traffic

Traffic congestion is usually observed at the upper stream of bottlenecks such as tunnels. Congestion appears as stop-and-go waves and high-density uniform flow. We perform simulations of traffic flow with a bottleneck using the coupled map optimal velocity model. The bottleneck is expressed as a road segment with speed reduction. The speed reduction in the bottleneck controls the emergence of stop-and-go waves. A phenomenological theory of bottleneck effects is constructed.

Construction of a matrix product stationary state from solutions of a finite-size system

Stationary states of stochastic models, which have N states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite M-dimensional matrix product stationary state for any {N, M}. Second, we give a method to construct the matrices from the stationary

Product Wave Function Renormalization Group: Construction from the Matrix Product Point of View

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T of a two-dimensional classical lattice model. A state vector created from the upper or the lower half of a finite size cluster approximates the largest-eigenvalue eigenvector. Decomposition of this state vector into the MPS gives a way of extending the MPS recursively. The extension process is a special case of the product wave function renormalization group (PWFRG) method, that accelerates the numerical calculation of the infinite system density matrix renormalization group (DMRG) method. As a result, we successfully give the physical interpretation of the PWFRG method, and obtain its appropriate initial condition.

Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow

Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.