Pallabi Dey | Searcharxiv

arXiv2026

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

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.

hep-lat↗

arXiv2025

Sign-problem landscape of dimer, loop, and ground state sectors of a U(1) quantum link model

The fermion sign problem poses a formidable challenge to the use of Monte Carlo methods for lattice gauge theories with dynamical fermionic matter fields. A meron cluster algorithm recently formulated for gauge fields represented as spin-$\frac{1}{2}$ quantum links coupled to a single flavour of staggered fermions samples only two of the exponentially many Gauss law (GL) sectors at low temperatures, allowing the simulation of those two GL sectors at zero temperature in polynomial time. In this article, we analytically identify GL sectors which can be simulated without encountering the fermion sign problem in arbitrary spatial dimensions. Using large-scale exact diagonalization and cluster Monte Carlo methods, we explore the nature of phases in the GL sectors dominating at zero temperature. The ground state lives in a superselection sector free of the sign problem, and maps to the quantum dimer model with mobile monomers. The usual zero-charge GL sector suffers from the fermion sign problem, and maps to the fully packed loop model with mobile monomers. The role of the magnetic energy in causing transitions between GL sectors is outlined. We expect our results to be valid for truncated Kogut-Susskind gauge theories, beyond quantum link models.

hep-lat↗