Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential

TL;DR

This paper introduces a method to approximate the quark contribution to the fermion free energy in lattice QCD at finite temperature and chemical potential, avoiding the sign problem at lowest order.

Contribution

The authors develop a nilpotency expansion approach that eliminates the sign problem in lattice QCD simulations at finite chemical potential.

Findings

Sign problem is absent at lowest order of the nilpotency expansion.

The derived expression allows Monte Carlo simulations without sign issues.

Applicable at zero temperature with potential for finite temperature extension.

Abstract

We have developed a method to derive the (approximate) quark contribution to the fermion free energy of QCD on a lattice, at finite temperature and chemical potential, with Kogut-Susskind fermions in the flavor basis. We show here the expression at zero temperature. This result has been obtained at the lowest order of the nilpotency expansion. At this order the well known "sign problem" does not arise and the quark contribution to the action can be used as a statistical weight in the Monte Carlo simulations.