Role of Plaquette Term in Genuine $2+1$D String Dynamics on Quantum Simulators

TL;DR

This paper investigates the role of the plaquette term in ensuring genuine 2+1D string dynamics in quantum simulators of lattice gauge theories, highlighting its importance for accurate simulation of higher-dimensional physics.

Contribution

It demonstrates that the plaquette term is essential for genuine 2+1D string dynamics and clarifies conditions under which string breaking can be effectively reduced to 1+1D processes.

Findings

Plaquette term is crucial for genuine 2+1D string dynamics.

Without the plaquette term, string breaking maps to 1+1D dynamics.

Guides future quantum simulation experiments of 2+1D LGTs.

Abstract

With the advent of quantum simulators of $2+1$D lattice gauge theories (LGTs), a fundamental open question is under what circumstances the observed physics is genuinely $2+1$D rather than effectively $1+1$D. Here, we address this question in the ongoing strong effort to quantum-simulate string dynamics in $2+1$D LGTs on state-of-the-art quantum hardware. Through tensor network simulations and analytic derivations, we show that the plaquette term, which represents a magnetic field and only emerges in $d>1$ spatial dimensions, plays a crucial role in \textit{genuine} $2+1$D string dynamics deep in the confined regime. In its absence and for minimal-length (Manhattan-distance) strings, we demonstrate how string breaking, although on a lattice in $d=2$ spatial dimensions, can be effectively mapped to a $1+1$D dynamical process independently of lattice geometry. Our findings not only answer the question of what qualifies as genuine $2+1$D string dynamics, but also serve as a clear guide for future quantum simulation experiments of $2+1$D LGTs.