Can rooted staggered fermions describe nonzero baryon density at low temperatures?

TL;DR

This paper investigates whether rooted staggered fermions can accurately describe nonzero baryon density at low temperatures, revealing a non-analytic behavior that complicates their use in QCD phase diagram studies.

Contribution

The study demonstrates a non-analyticity in baryon density predictions with rooted staggered fermions at low temperatures and nonzero chemical potential, highlighting potential limitations of this discretization.

Findings

Sharp rise in baryon density at specific chemical potential

Non-analyticity differs from pion condensation transition

Effect diminishes on finer lattices for two flavors

Abstract

Research on the QCD phase diagram with lattice field theory methods is dominated by the use of rooted staggered fermions, as they are the computationally cheapest discretization available. We show that rooted staggered fermions at a nonzero baryochemical potential $\mu_B$ predict a sharp rise in the baryon density at low temperatures and $\mu_B \gtrsim 3 m_\pi/2$, where $m_\pi$ is the Goldstone pion mass. We elucidate the nature of the non-analyticity behind this sharp rise in the density by a comparison of reweighting results with a Taylor expansion of high order. While at first sight this non-analytic behavior becomes apparent at the same position where the pion condensation transition takes place in the phase-quenched theory, the nature of the non-analyticity in the two theories appears to be quite different: While at nonzero isospin density the data are consistent with a genuine thermodynamic (branch-point) singularity, the results at nonzero baryon density point to an essential singularity at $\mu_B=0$. The effect is absent for four flavors of degenerate quarks, where rooting is not used. For the two-flavor case, we show numerical evidence that the magnitude of the effect diminishes on finer lattices. We discuss the implications of this technical complication on future studies of the QCD phase diagram.