87 research outputs found
Universal and non-universal behavior in Dirac spectra
We have computed ensembles of complete spectra of the staggered Dirac
operator using four-dimensional SU(2) gauge fields, both in the quenched
approximation and with dynamical fermions. To identify universal features in
the Dirac spectrum, we compare the lattice data with predictions from chiral
random matrix theory for the distribution of the low-lying eigenvalues. Good
agreement is found up to some limiting energy, the so-called Thouless energy,
above which random matrix theory no longer applies. We determine the dependence
of the Thouless energy on the simulation parameters using the scalar
susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure
Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory
We calculate complete spectra of the Kogut-Susskind Dirac operator on the
lattice in quenched SU(3) gauge theory for various values of coupling constant
and lattice size. From these spectra we compute the connected and disconnected
scalar susceptibilities and find agreement with chiral random matrix theory up
to a certain energy scale, the Thouless energy. The dependence of this scale on
the lattice volume is analyzed. In the case of the connected susceptibility
this dependence is anomalous, and we explain the reason for this. We present a
model of chiral perturbation theory that is capable of describing the data
beyond the Thouless energy and that has a common range of applicability with
chiral random matrix theory.Comment: 8 pages, RevTeX, 15 .eps figure
Randomness on the Lattice
In this lecture we review recent lattice QCD studies of the statistical
properties of the eigenvalues of the QCD Dirac operator. We find that the
fluctuations of the smallest Dirac eigenvalues are described by chiral Random
Matrix Theories with the global symmetries of the QCD partition function.
Deviations from chiral Random Matrix Theory beyond the Thouless energy can be
understood analytically by means of partially quenched chiral perturbation
theory.Comment: Invited talk at the International Light-Cone Meeting on
Non-Perturbative QCD and Hadron Phenomenology, Heidelberg 12-17 June 2000. 12
pages, 7 figures, Late
Kramers Equation Algorithm with Kogut-Susskind Fermions on Lattice
We compare the performance of the Kramers Equation Monte Carlo (KMC)
Algorithm with that of the Hybrid Monte Carlo (HMC) algorithm for numerical
simulations with dynamical Kogut-Susskind fermions. Using the lattice
Gross-Neveu model in 2 space-time dimensions, we calculate the integrated
autocorrelation time of different observables at a number of couplings in the
scaling region on 16^2 and 32^2 lattices while varying the parameters of the
algorithms for optimal performance. In our investigation the performance of KMC
is always significantly below than that of HMC for the observables used. We
also stress the importance of having a large number of configurations for the
accurate estimation of the integrated autocorrelation time.Comment: revised version to appear in Phys. Lett. B, 9 pages, 3 ps figure
Spectral correlations of the massive QCD Dirac operator at finite temperature
We use the graded eigenvalue method, a variant of the supersymmetry
technique, to compute the universal spectral correlations of the QCD Dirac
operator in the presence of massive dynamical quarks. The calculation is done
for the chiral Gaussian unitary ensemble of random matrix theory with an
arbitrary Hermitian matrix added to the Dirac matrix. This case is of interest
for schematic models of QCD at finite temperature.Comment: 19 pages, no figures, LaTeX (elsart.cls) minor changes, one reference
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Comparing lattice Dirac operators with Random Matrix Theory
We study the eigenvalue spectrum of different lattice Dirac operators
(staggered, fixed point, overlap) and discuss their dependence on the
topological sectors. Although the model is 2D (the Schwinger model with
massless fermions) our observations indicate possible problems in 4D
applications. In particular misidentification of the smallest eigenvalues due
to non-identification of the topological sector may hinder successful
comparison with Random Matrix Theory (RMT).Comment: LATTICE99(topology and confinement), Latex2e using espcrc2.sty, 3
pages, 3 figure
Can we do better than Hybrid Monte Carlo in Lattice QCD?
The Hybrid Monte Carlo algorithm for the simulation of QCD with dynamical
staggered fermions is compared with Kramers equation algorithm. We find
substantially different autocorrelation times for local and nonlocal
observables. The calculations have been performed on the parallel computer CRAY
T3D.Comment: Talk presented at LATTICE96(algorithms), LaTeX 3 pages, uses espcrc2,
epsf, 2 postscript figure
Determining F_pi from spectral sum rules
We derive spectral sum rules for a system with two quarks coupled to an
imaginary isospin chemical potential in the \epsilon regime. The sum rules show
an explicit dependence on the pion decay constant which should make it possible
to measure F_pi from the eigenvalue spectrum of this particular Dirac operator.Comment: 8 page
Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
We have calculated complete spectra of the staggered Dirac operator on the
lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice
sizes. The microscopic spectral density, the distribution of the smallest
eigenvalue, and the two-point spectral correlation function are analyzed. We
find the expected agreement of the lattice data with universal predictions of
the chiral unitary ensemble of random matrix theory up to a certain energy
scale, the Thouless energy. The deviations from the universal predictions are
determined using the disconnected scalar susceptibility. We find that the
Thouless energy scales with the lattice size as expected from theoretical
arguments making use of the Gell-Mann--Oakes--Renner relation.Comment: REVTeX, 5 pages, 4 figure
Chiral Random Matrix Model for Critical Statistics
We propose a random matrix model that interpolates between the chiral random
matrix ensembles and the chiral Poisson ensemble. By mapping this model on a
non-interacting Fermi-gas we show that for energy differences less than a
critical energy the spectral correlations are given by chiral Random
Matrix Theory whereas for energy differences larger than the number
variance shows a linear dependence on the energy difference with a slope that
depends on the parameters of the model. If the parameters are scaled such that
the slope remains fixed in the thermodynamic limit, this model provides a
description of QCD Dirac spectra in the universality class of critical
statistics. In this way a good description of QCD Dirac spectra for gauge field
configurations given by a liquid of instantons is obtained.Comment: 21 pages, 3 figures, Latex; added two references and minor
correction
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