72 research outputs found
A systematic way to find and construct exact finite dimensional matrix product stationary states
We explain how to construct matrix product stationary states which are
composed of finite-dimensional matrices. Our construction explained in this
article was first presented in a part of [Hieida and Sasamoto:J. Phys. A: Math.
Gen. 37 (2004) 9873] for general models. In this article, we give more details
on the treatment than in the above-mentioned reference, for one-dimensional
asymmetric simple exclusion process(ASEP).Comment: This article will appear in the proceedings of "Workshop on Matrix
Product State Formulation and Density Matrix Renormalization Group
Simulations (MPS&DMRG)" to be published by World Scientifi
Universal Asymptotic Eigenvalue Distribution of Density Matrices and the Corner Transfer Matrices in the Thermodynamic Limit
We study the asymptotic behavior of the eigenvalue distribution of the
Baxter's corner transfer matrix (CTM) and the density matrix (DM) in the
White's density-matrix renormalization group (DMRG), for one-dimensional
quantum and two-dimensional classical statistical systems. We utilize the
relationship which holds for non-critical systems in the
thermodynamic limit. Using the known diagonal form of CTM, we derive exact
asymptotic form of the DM eigenvalue distribution for the integrable
XXZ chain (and its related integrable models) in the massive regime. The result
is then recast into a ``universal'' form without model-specific quantities,
which leads to for -th DM
eigenvalue at larg . We perform numerical renormalization group calculations
(using the corner-transfer-matrix RG and the product-wavefunction RG) for
non-integrable models, verifying the ``universal asymptotic form'' for them.
Our results strongly suggest the universality of the asymptotic eigenvalue
distribution of DM and CTM for a wide class of systems.Comment: 4 pages, RevTeX, 4 ps figure
Numerical Renormalization Approach to Two-Dimensional Quantum Antiferromagnets with Valence-Bond-Solid Type Ground State
We study the ground-state properties of the two-dimensional quantum spin
systems having the valence-bond-solid (VBS) type ground states. The
``product-of-tensors'' form of the ground-state wavefunction of the system is
utilized to associate it with an equivalent classical lattice statistical model
which can be treated by the transfer-matrix method. For diagonalization of the
transfer matrix, we employ the product-wavefunction renormalization group
method which is a variant of the density-matrix renormalization group method.
We obtain the correlation length and the sublattice magnetization accurately.
For the anisotropically ``deformed'' S=3/2 VBS model on the honeycomb lattice,
we find that the correlation length as a function of the deformation parameter
behaves very much alike as that in the S=3/2 VBS chain.Comment: 9 pages and 11 non-embedded figures, REVTex, submitted to New Journal
of Physic
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.Comment: 8 pages, 6 figures, EPJB accepte
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.Comment: 9 pages, 4 figures, submitted to Prog. Theor. Phy
Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz
We present a new algorithm to calculate the thermodynamic quantities of
three-dimensional (3D) classical statistical systems, based on the ideas of the
tensor product state and the density matrix renormalization group. We represent
the maximum-eigenvalue eigenstate of the transfer matrix as the product of
local tensors which are iteratively optimized by the use of the ``vertical
density matrix'' formed by cutting the system along the transfer direction.
This algorithm, which we call vertical density matrix algorithm (VDMA), is
successfully applied to the 3D Ising model. Using the Suzuki-Trotter
transformation, we can also apply the VDMA to two-dimensional (2D) quantum
systems, which we demonstrate for the 2D transverse field Ising model.Comment: Unnecessary files are removed. 8 pages, 7 figures, submitted to
Phys.Rev.
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.Comment: 12 pages, 6 figure
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