Cluster-Algorithm-Amenable Models of Gauge Fields and Matter

TL;DR

This paper introduces new cluster algorithms for simulating fermions coupled to gauge fields without the sign problem, enabling efficient exploration of complex phase diagrams relevant for quantum simulations.

Contribution

It develops novel cluster algorithms and models for fermions with gauge fields that are sign-problem free, facilitating more efficient simulations.

Findings

Cluster algorithms successfully simulate fermions with gauge fields.

Models exhibit rich phase diagrams.

Simulations are relevant for quantum experiments.

Abstract

Typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on cluster algorithms which do not involve the determinant and involve a more physically relevant sampling of the configuration space. We develop new cluster algorithms and design classes of models for fermions coupled to $\mathbb{Z}_2$ and $U(1)$ gauge fields that are amenable to being simulated by these cluster algorithms in a sign-problem free way. Such simulations should contain rich phase diagrams and are particularly relevant for quantum simulator experiments.