Meron-Cluster Solution of Fermion Sign Problems

TL;DR

This paper introduces a cluster algorithm approach to effectively solve the fermion sign problem across various fermionic systems, including Hubbard models and relativistic fermions, by decomposing configurations into independent clusters.

Contribution

It develops a general cluster algorithm framework that isolates meron-clusters, enabling exact solutions to the fermion sign problem in multiple fermionic models.

Findings

The method successfully eliminates the sign problem in tested models.

Configurations with meron-clusters contribute zero, simplifying calculations.

The approach provides a new way to simulate fermionic systems efficiently.

Abstract

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for non-relativistic lattice fermions. A configuration of fermion world-lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron-clusters contribute 0 to the path integral, while all other configurations contribute 1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.