Thermodynamics of free Domain Wall fermions

TL;DR

This paper analyzes thermodynamic properties of free domain wall fermions, identifying minimal lattice corrections at certain parameters, proposing modifications to reduce finite cut-off effects, and examining the impact of chemical potential on divergences and chiral symmetry.

Contribution

It introduces modifications to domain wall and overlap operators to minimize finite cut-off effects and studies thermodynamic quantities with chemical potential in free domain wall fermions.

Findings

Lattice corrections are minimized for N_T≥10 with specific M range.

Proposed modifications reduce finite cut-off effects to within 10%.

μ² divergences are absent for many domain wall fermion actions despite chiral symmetry breaking.

Abstract

Studying various thermodynamic quantities for the free domain wall fermions for both finite and infinite fifth dimensional extent N_5, we find that the lattice corrections are minimum for $N_T\geq10$ for both energy density and susceptibility, for its irrelevant parameter M in the range 1.45-1.50. The correction terms are, however, quite large for small lattice sizes of $N_T\leq8$. We propose modifications of the domain wall operator, as well as the overlap operator, to reduce the finite cut-off effects to within 10% of the continuum results of the thermodynamic quantities for the currently used N_T=6-8 lattices. Incorporating chemical potential, we show that \mu^2 divergences are absent for a large class of such domain wall fermion actions although the chiral symmetry is broken for $\mu\neq0$.