The density of states approach to dense quantum systems

TL;DR

This paper introduces a generalized density of states method to numerically study quantum field theories with complex actions, successfully addressing the sign problem in finite density models and enabling new simulations of dense quantum systems.

Contribution

The authors develop a novel density of states approach that overcomes the sign problem in quantum field theories, demonstrated on the $Z_3$ spin model at finite density.

Findings

Successfully solved the sign problem in the $Z_3$ spin model.

Confirmed results with dual theory simulations free from sign problems.

Paves the way for ab initio simulations of dense quantum systems.

Abstract

We develop a first-principle generalised density of state method for studying numerically quantum field theories with a complex action. As a proof of concept, we show that with our approach we can solve numerically the strong sign problem of the $Z_3$ spin model at finite density. Our results are confirmed by standard simulations of the theory dual to the considered model, which is free from a sign problem. Our method opens new perspectives on ab initio simulations of cold dense quantum systems, and in particular of Yang-Mills theories with matter at finite densities, for which Monte Carlo based importance sampling are unable to produce sufficiently accurate results.