arXiv subjects

H. Hehl

Publications and source records attributed to H. Hehl.

6 recordsLinked to original sources

arXiv2001

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.

hep-lat↗

arXiv2000

Dirac eigenvalues and eigenvectors at finite temperature

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.

hep-lat↗

arXiv1999

Beyond the Thouless energy

The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy $E_c\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly $1/V<E<1/\sqrt{V}$, where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important to take into account only those symmetries which are exactly realized on the lattice.

hep-lat↗

arXiv1999

Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data

Recently, the chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that the deviations of lattice results from random matrix theory starting around the so-called Thouless energy can be understood in terms of chiral perturbation theory as well. Comparison of lattice data with chiral perturbation theory formulae allows us to compute the pion decay constant. We present results from a calculation for quenched SU(2) with Kogut-Susskind fermions at β=2.0 and 2.2.

hep-lat↗

arXiv1999

Random Matrix Theory and Chiral Logarithms

Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m*log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).

hep-lat↗

arXiv1998

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 β= 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.

hep-lat↗