1,093 research outputs found
From Random Matrices to Stochastic Operators
We propose that classical random matrix models are properly viewed as finite
difference schemes for stochastic differential operators. Three particular
stochastic operators commonly arise, each associated with a familiar class of
local eigenvalue behavior. The stochastic Airy operator displays soft edge
behavior, associated with the Airy kernel. The stochastic Bessel operator
displays hard edge behavior, associated with the Bessel kernel. The article
concludes with suggestions for a stochastic sine operator, which would display
bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics.
Changes in this revision: recomputed Monte Carlo simulations, added reference
[19], fit into margins, performed minor editin
Path integral Monte Carlo simulations of silicates
We investigate the thermal expansion of crystalline SiO in the --
cristobalite and the -quartz structure with path integral Monte Carlo
(PIMC) techniques. This simulation method allows to treat low-temperature
quantum effects properly. At temperatures below the Debye temperature, thermal
properties obtained with PIMC agree better with experimental results than those
obtained with classical Monte Carlo methods.Comment: 27 pages, 10 figures, Phys. Rev. B (in press
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 -dimensional space. The
Hamiltonians contain only nearest neighbor interactions whose strength is
proportional to , where is the lattice index and where
is a deformation parameter. In the limit 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 Heisenberg spin chain by use of the
density matrix renormalization group (DMRG) method. It is shown that the ground
state is dimerized when is finite. Spin correlation function show
exponential decay, and the boundary effect decreases with increasing .Comment: 5 pages, 4 figure
Impurity corrections to the thermodynamics in spin chains using a transfer-matrix DMRG method
We use the density matrix renormalization group (DMRG) for transfer matrices
to numerically calculate impurity corrections to thermodynamic properties. The
method is applied to two impurity models in the spin-1/2 chain, namely a weak
link in the chain and an external impurity spin. The numerical analysis
confirms the field theory calculations and gives new results for the crossover
behavior.Comment: 9 pages in revtex format including 5 embedded figures (using epsf).
To appear in PRB. The latest version in PDF format can be found at
http://fy.chalmers.se/~eggert/papers/DMRGimp.pd
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.Comment: 15 pages, uses IOP styl
Thermodynamics of a one-dimensional S=1/2 spin-orbital model
The thermodynamic properties of a one-dimensional model describing spin
dynamics in the presence of a twofold orbital degeneracy are studied
numerically using the transfer-matrix renormalization group (TMRG). The model
contains an integrable SU(4)-symmetric point and a gapless phase which is SU(4)
invariant up to a rescaling of the velocities for spin and orbital degrees of
freedom which allows detailed comparison of the numerical results with
conformal field theory. We pay special attention to the correlation lengths
which show an intriguing evolution with temperature. We find that the model
shows an intrinsic tendency towards dimerization at finite temperature even if
the ground state is not dimerized.Comment: 9 pages, 12 figure
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, for the purpose of
rapidly performing the infinite system density matrix renormalization group
(DMRG) method applied to two-dimensional classical lattice models. We use the
fact that the largest-eigenvalue eigenvector of T can be approximated by a
state vector created from the upper or lower half of a finite size cluster.
Decomposition of the obtained state vector into the MPS gives a way of
extending the MPS, at the system size increment process in the infinite system
DMRG algorithm. As a result, we successfully give the physical interpretation
of the product wave function renormalization group (PWFRG) method, and obtain
its appropriate initial condition.Comment: 8 pages, 8 figure
Staggered dimer order in S=1/2 quantum spin ladder system with four spin exchange
We study the S=1/2 quantum spin ladder system with the four-spin exchange,
using density matrix renormalization group method and an exact diagonalization
method. Recently, the phase transition in this system and its universality
class are studied. But there remain controversies whether the phase transition
is second order type or the other type and the nature of order parameter. There
are arguments that the massless phase appears. But this does not agree with our
previous result. Analyzing DMRG data, we try a new approach in order to
determine a phase which appears after the phase transition. We find that the
edge state appears in the open boundary condition, investigating excitation
energies of states with higher magnetizations.Comment: Submitted to Phys. Rev. B, (REVTeX4
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