The density in the density of states method

TL;DR

This paper investigates the phase angle distribution in QCD at finite baryon density, revealing that non-Gaussian deviations, though small, can significantly affect the density of states method's results.

Contribution

It demonstrates that non-Gaussian terms in the phase angle distribution arise from lattice effects and can impact observables in the density of states approach.

Findings

Gaussian distribution from hadron resonance gas model

Deviations from Gaussian form due to lattice effects

Non-Gaussian terms significantly influence observables

Abstract

It has been suggested that for QCD at finite baryon density the distribution of the phase angle, i.e. the angle defined as the imaginary part of the logarithm of the fermion determinant, has a simple Gaussian form. This distribution provides the density in the density of states approach to the sign problem. We calculate this phase angle distribution using i) the hadron resonance gas model; and ii) a combined strong coupling and hopping parameter expansion in lattice gauge theory. While the former model leads only to a Gaussian distribution, in the latter expansion we discover terms which cause the phase angle distribution to deviate, by relative amounts proportional to powers of the inverse lattice volume, from a simple Gaussian form. We show that despite the tiny inverse-volume deviation of the phase angle distribution from a simple Gaussian form, such non-Gaussian terms can have a substantial impact on observables computed in the density of states/reweighting approach to the sign problem.