Density of states techniques for fermion worldlines

TL;DR

This paper introduces a density of states method for fermion worldlines to address the sign problem at finite density, demonstrating initial numerical results in two dimensions.

Contribution

It develops a novel density of states approach for fermionic worldlines that handles sign issues in finite density lattice field theories.

Findings

First implementation in 2D shows promising results.

Fixed winding number approach effectively manages sign problem.

Method paves the way for more accurate fermionic simulations.

Abstract

Worldline representations were established as a powerful tool for studying bosonic lattice field theories at finite density. For fermions, however, the worldlines still may carry signs that originate from the Dirac algebra and from the Grassmann nature of the fermion fields. We show that a density of states approach can be set up to deal with this remaining sign problem, where finite density is implemented in a canonical approach by working with a fixed winding number of the fermion worldlines. We discuss the approach in detail and show first results of a numerical implementation in 2 dimensions.