Repulsively Bound Hadrons in a $\mathbb{Z}_2$ Lattice Gauge Theory

TL;DR

This paper demonstrates the existence of stable, repulsively bound hadron states in a $ ext{Z}_2$ lattice gauge theory, revealing new dynamical binding mechanisms and potential for experimental observation.

Contribution

It introduces a novel dynamical binding mechanism for hadrons in a $ ext{Z}_2$ gauge theory, including repulsively bound states stabilized by quantum fluctuations.

Findings

Revealed stable repulsively bound hadron states.

Identified two mechanisms for hadron formation: attraction and repulsion.

Provided numerical simulations and an effective model explaining the bound states.

Abstract

The $\mathbb{Z}_2$ lattice gauge theory is a paradigmatic model that exhibits gauge-field-mediated-confinement of pairs of particles into mesons, drawing connections to quantum chromodynamics. In the absence of any additional attractive interactions between particles, mesons are not known to bind in this model. Here, we show that resonant pair-production terms give rise to two separate mechanisms to form stable ``hadron'' bound states of two mesons: either induced by an effective attractive interaction, or a new dynamical binding mechanism induced by an effective repulsion. The repulsively bound hadron is a high-energy state stabilized by being energetically separated from the two-meson continuum through quantum fluctuations of the gauge fields. We study the dynamical formation of this bound state starting from local excitations. We use matrix product state techniques based on the time-evolving block decimation algorithm to perform our numerical simulations and analyze the effect of model parameters on hadron formation. Furthermore, we derive an effective model that explains its formation. Our findings are amenable to experimental observation on modern quantum hardware such as superconducting qubits, trapped ions, and Rydberg atom arrays.