The density of states approach to the sign problem

TL;DR

This paper reviews the density of states approach to the sign problem, highlighting the LLR algorithm's ability to compute the density with reduced error, and discusses its application to the four-dimensional Bose gas.

Contribution

It demonstrates the application of the LLR algorithm to the Bose gas, analyzing systematic errors and bias control in the density of states method.

Findings

Successful application of LLR to 4D Bose gas

Identification of systematic errors in the method

Strategies for bias control in density of states calculations

Abstract

Approaches to the sign problem based on the density of states have been recently revived by the introduction of the LLR algorithm, which allows us to compute the density of states itself with exponential error reduction. In this work, after a review of the generalities of the method, we show recent results for the Bose gas in four dimensions, focussing on the identification of possible systematic errors and on methods of controlling the bias they can introduce in the calculation.