Realistic scheme for quantum simulation of $\mathbb{Z}_2$ lattice gauge theories with dynamical matter in $(2+1)$D

TL;DR

This paper proposes a feasible Rydberg atom array scheme to simulate $(2+1)$D $ ext{Z}_2$ lattice gauge theories with dynamical matter, enabling experimental exploration of complex quantum phases and transitions.

Contribution

It introduces a realistic, local-interaction-based scheme for simulating $ ext{Z}_2$ gauge theories with dynamical matter in two dimensions using Rydberg atoms, including derivation of effective Hamiltonians.

Findings

Derivation of effective Hamiltonians for $ ext{Z}_2$ gauge theories with matter.

Identification of ground-state phase diagrams with spin liquid phases.

Proposals for experimental probes of localization and deconfinement.

Abstract

Gauge fields coupled to dynamical matter are ubiquitous in many disciplines of physics, ranging from particle to condensed matter physics, but their implementation in large-scale quantum simulators remains challenging. Here we propose a realistic scheme for Rydberg atom array experiments in which a $\mathbb{Z}_2$ gauge structure with dynamical charges emerges on experimentally relevant timescales from only local two-body interactions and one-body terms in two spatial dimensions. The scheme enables the experimental study of a variety of models, including $(2+1)$D $\mathbb{Z}_2$ lattice gauge theories coupled to different types of dynamical matter and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally most relevant effective $\mathbb{Z}_2$ lattice gauge theories with dynamical matter featuring various confined and deconfined, quantum spin liquid phases. Further, we present selected probes with immediate experimental relevance, including signatures of disorder-free localization and a thermal deconfinement transition of two charges.