Form the density-of-states method to finite density quantum field theory

TL;DR

This paper introduces the LLR density-of-states method and its extension to complex actions, offering a promising approach to overcome overlap and sign problems in finite density quantum field theories, demonstrated through various gauge theories and models.

Contribution

The paper presents the LLR density-of-states method and its generalization to complex actions, providing a new tool for finite density QFT simulations.

Findings

Successfully applied to U(1), SU(2), SU(3) gauge theories

Effective in addressing overlap and sign problems

Demonstrated on Z3 spin model and heavy-dense QCD

Abstract

During the last 40 years, Monte Carlo calculations based upon Importance Sampling have matured into the most widely employed method for determinig first principle results in QCD. Nevertheless, Importance Sampling leads to spectacular failures in situations in which certain rare configurations play a non-secondary role as it is the case for Yang-Mills theories near a first order phase transition or quantum field theories at finite matter density when studied with the re-weighting method. The density-of-states method in its LLR formulation has the potential to solve such overlap or sign problems by means of an exponential error suppression. We here introduce the LLR approach and its generalisation to complex action systems. Applications include U(1), SU(2) and SU(3) gauge theories as well as the Z3 spin model at finite densities and heavy-dense QCD.