The density of states approach for the simulation of finite density quantum field theories

TL;DR

This paper reviews recent advances in using the density-of-states approach, combined with Wang-Landau techniques, to simulate finite density quantum field theories despite the sign problem, focusing on high-precision calculations and dual formulations.

Contribution

It introduces high-precision density-of-states calculations and demonstrates progress in extracting reliable results from highly oscillating integrals in finite density quantum field theories.

Findings

Density-of-states can be computed over hundreds of orders of magnitude.

Recent progress enables reliable results from highly oscillating integrals.

Simulation of the dual $Z_3$ theory avoids the sign problem.

Abstract

Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type simulation techniques and recent advances, the density-of-states can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the state-of-play for the high precision calculations of the density-of-states as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the $Z_3$ quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to free of a sign problem.