2,691 research outputs found
The Density Matrix Renormalization Group technique with periodic boundary conditions
The Density Matrix Renormalization Group (DMRG) method with periodic boundary
conditions is introduced for two dimensional classical spin models. It is shown
that this method is more suitable for derivation of the properties of infinite
2D systems than the DMRG with open boundary conditions despite the latter
describes much better strips of finite width. For calculation at criticality,
phenomenological renormalization at finite strips is used together with a
criterion for optimum strip width for a given order of approximation. For this
width the critical temperature of 2D Ising model is estimated with seven-digit
accuracy for not too large order of approximation. Similar precision is reached
for critical indices. These results exceed the accuracy of similar calculations
for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.
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.Comment: 8 pages, LaTeX (using jpsj.sty), 4 non-embedded figures, submitted to
J. Phys. Soc. Jp
Incommensurate structures studied by a modified Density Matrix Renormalization Group Method
A modified density matrix renormalization group (DMRG) method is introduced
and applied to classical two-dimensional models: the anisotropic triangular
nearest- neighbor Ising (ATNNI) model and the anisotropic triangular
next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have
complex structures and exhibit incommensurate phases. It was found that the
incommensurate phase completely separates the disordered phase from one of the
commensurate phases, i. e. the non-existence of the Lifshitz point in phase
diagrams of both models was confirmed.Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB,
presented at MECO'24 1999 (Wittenberg, Germany
Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures
We introduce a systematic method for constructing a class of lattice
structures that we call ``partial line graphs''.In tight-binding models on
partial line graphs, energy bands with flat energy dispersions emerge.This
method can be applied to two- and three-dimensional systems. We show examples
of partial line graphs of square and cubic lattices. The method is useful in
providing a guideline for synthesizing materials with flat energy bands, since
the tight-binding models on the partial line graphs provide us a large room for
modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure
A Density Matrix Algorithm for 3D Classical Models
We generalize the corner transfer matrix renormalization group, which
consists of White's density matrix algorithm and Baxter's method of the corner
transfer matrix, to three dimensional (3D) classical models. The
renormalization group transformation is obtained through the diagonalization of
density matrices for a cubic cluster. A trial application for 3D Ising model
with m=2 is shown as the simplest case.Comment: 15 pages, Latex(JPSJ style files are included), 8 ps figures,
submitted to J. Phys. Soc. Jpn., some references are correcte
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 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.Comment: 4 pages, 3 figure
Thermodynamic properties of the one-dimensional Kondo insulators studied by the density matrix renormalization group method
Thermodynamic properties of the one-dimensional Kondo lattice model at
half-filling are studied by the density matrix renormalization group method
applied to the quantum transfer matrix. Spin susceptibility, charge
susceptibility, and specific heat are calculated down to T=0.1t for various
exchange constants. The obtained results clearly show crossover behavior from
the high temperature regime of nearly independent localized spins and
conduction electrons to the low temperature regime where the two degrees of
freedom couple strongly. The low temperature energy scales of the charge and
spin susceptibilities are determined and shown to be equal to the quasiparticle
gap and the spin gap, respectively, for weak exchange couplings.Comment: 4 pages, 3 Postscript figures, REVTeX, submitted to J. Phys. Soc. Jp
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.Comment: 21 pages, Latex, 14 figures in postscript files, Proc. of the 1996 El
Escorial Summer School on "Strongly Correlated Magnetic and Superconducting
Systems
On zero modes of the eleven dimensional superstring
It is shown that recently pointed out by Berkovits on-shell degrees of
freedom of the D=11 superstring do not make contributions into the quantum
states spectrum of the theory. As a consequence, the spectrum coincides with
that of the D=10 type IIA superstring.Comment: 7 pages, LaTex fil
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