Confinement in 1+1D $\mathbb{Z}_2$ Lattice Gauge Theories at Finite Temperature

TL;DR

This paper investigates confinement phenomena in a 1+1D $ ext{Z}_2$ lattice gauge theory at finite temperature using matrix product states, revealing a crossover between confined and deconfined regimes and confirming the persistence of mesons.

Contribution

It introduces a comprehensive study of confinement at finite temperature in a simple 1D $ ext{Z}_2$ gauge theory, combining MPS calculations with experimental observables.

Findings

Identifies a smooth crossover between confined and deconfined phases.

Shows mesons remain well-defined at arbitrary finite temperatures.

Validates results with quench dynamics via exact diagonalization.

Abstract

Confinement is a paradigmatic phenomenon of gauge theories, and its understanding lies at the forefront of high-energy physics. Here, we study confinement in a simple one-dimensional $\mathbb{Z}_2$ lattice gauge theory at finite temperature and filling, which is within the reach of current cold-atom and superconducting-qubit platforms. By employing matrix product states (MPS) calculations, we investigate the decay of the finite-temperature Green's function and uncover a smooth crossover between the confined and deconfined regimes. Furthermore, using the Friedel oscillations and string length distributions obtained from snapshots sampled from MPS, both of which are experimentally readily available, we verify that confined mesons remain well-defined at arbitrary finite temperature. This phenomenology is further supported by probing quench dynamics of mesons with exact diagonalization. Our results shed new light on confinement at finite temperature from an experimentally relevant standpoint.