String Breaking in a $2+1$D $\mathbb{Z}_2$ Lattice Gauge Theory

TL;DR

This paper uses matrix product state simulations to analyze string breaking in a 2+1D $ ext{Z}_2$ lattice gauge theory, revealing mechanisms and dualities relevant for experiments with quantum computers.

Contribution

It provides a detailed microscopic analysis of string breaking in 2+1D $ ext{Z}_2$ LGTs, including the role of magnetic fluctuations and a duality to free fermions.

Findings

Magnetic fluctuations stabilize the strings.

Deep in the confined regime, the system maps to free fermions.

Results are experimentally accessible with superconducting qubits.

Abstract

String breaking is an intriguing phenomenon crucial to the understanding of lattice gauge theories (LGTs), with strong relevance to both condensed matter and high-energy physics (HEP). Recent experiments investigating string breaking in $2+1$D (two spatial and one temporal dimensions) LGTs motivate a thorough analysis of its underlying mechanisms. Here, we perform matrix product state (MPS) simulations of string breaking in an experimentally relevant $2+1$D $\mathbb{Z}_2$ LGT in the presence of two external charges. We provide a detailed description of the system in the confined phase, highlight a number of mechanisms which are responsible for string breaking, and argue that magnetic fluctuations have a stabilizing effect on the strings. Moreover, we show that deep in the confined regime the problem is dual to one-dimensional free fermions hopping on an open chain. Our work elucidates the microscopic processes of string breaking in $2+1$D LGTs, and our findings can be probed on current superconducting-qubit quantum computers.