Breakdown of staggered fermions at nonzero chemical potential

TL;DR

This paper addresses the phase ambiguities in the staggered fermion determinant at nonzero chemical potential and proposes a resolution method that is effective near the continuum limit, highlighting limitations at larger chemical potentials.

Contribution

The authors introduce a method to resolve phase ambiguities in the staggered fermion determinant at nonzero chemical potential, applicable close to the continuum limit.

Findings

Phase ambiguities can be resolved near the continuum limit.

The method is limited to small Re mu, close to the continuum.

Breakdown occurs when Re mu exceeds about half the pion mass at zero temperature.

Abstract

The staggered fermion determinant is complex when the quark chemical potential mu is nonzero. Its fourth root, used in simulations with dynamical fermions, will have phase ambiguities that become acute when Re mu is sufficiently large. We show how to resolve these ambiguities, but our prescription only works very close to the continuum limit. We argue that this regime is far from current capabilities. Other procedures require being even closer to the continuum limit, or fail altogether, because of unphysical discontinuities in the measure. At zero temperature the breakdown is expected when Re mu is greater than approximately half the pion mass. Estimates of the location of the breakdown at nonzero temperature are less certain.