Interplay of Gauss Law and the fermion sign problem in quantum link models with dynamical matter

TL;DR

This paper investigates the ground state properties of quantum link models with dynamical matter, showing that certain sectors are free of the fermion sign problem and proposing a cluster algorithm for efficient sampling.

Contribution

It identifies a specific Gauss Law sector free of the fermion sign problem and introduces a meron cluster algorithm for sampling ground states in these models.

Findings

Ground state lies in a sector satisfying (G_e,G_o) = (d, -d)

This sector is free of the fermion sign problem

A meron cluster algorithm effectively samples ground states

Abstract

Quantum Link Models with dynamical matter coupled to spin-$\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies $(G_e,G_o) = (d,\ -d)$, where $d$ is the spatial dimension and $e$ and $o$ are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.