String Breaking Dynamics and Glueball Formation in a $2+1$D Lattice Gauge Theory

TL;DR

This paper investigates the real-time dynamics of electric flux strings and glueball-like formations in a 2+1D lattice gauge theory using tensor network methods, providing insights relevant for quantum simulation experiments.

Contribution

It introduces a detailed study of string breaking and glueball formation in 2+1D $ ext{Z}_2$ lattice gauge theory, connecting tensor network simulations with potential quantum computing realizations.

Findings

Identification of string breaking processes at resonances.

Characterization of confined string dynamics under strong fields.

Observation of glueball-like loop formations during string splitting.

Abstract

With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the $2+1$D $\mathbb{Z}_2$ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.