Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

TL;DR

This paper investigates how improving fermion dispersion relations in lattice QCD reduces cut-off effects in thermodynamic calculations at high temperature and chemical potential, providing explicit corrections and comparisons across fermion types.

Contribution

It demonstrates that rotational invariance of the quark propagator up to a certain order can eliminate cut-off effects in thermodynamic observables at high temperature and chemical potential.

Findings

Cut-off effects can be eliminated up to O(a^n) in dispersion relations.

Finite cut-off corrections depend on Bernoulli polynomials, independent of discretization scheme.

Explicit calculations compare staggered, Wilson, overlap, and domain wall fermions.

Abstract

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to O(a^n) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show, that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations.