Fractionalized holes in one-dimensional $\mathbb{Z}_2$ gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability

TL;DR

This paper explores the dynamics of fractionalized holes in a one-dimensional $ ext{Z}_2$ gauge theory coupled to fermions, revealing emergent integrability, deconfined excitations, and novel ground states near specific fillings.

Contribution

It uncovers emergent integrable correlated hopping of holes and analyzes their dynamics and entanglement, providing new insights into fractionalized excitations in gauge-fermion systems.

Findings

Emergent integrable correlated hopping dynamics of holes.

Deconfined hole excitations near filling $ u^h=1/3$.

Numerical and analytical characterization of hole spreading and entanglement evolution.

Abstract

We investigate the interplay of quantum one-dimensional discrete $\mathbb{Z}_2$ gauge fields and fermion matter near full filling in terms of deconfined fractionalized hole excitations that constitute mobile domain walls between vacua that break spontaneously translation symmetry. In the limit of strong string tension, we uncover emergent integrable correlated hopping dynamics of holes which is complementary to the constrained XXZ description in terms of bosonic dimers. We analyze numerically quantum dynamics of spreading of an isolated hole together with the associated time evolution of entanglement and provide analytical understanding of its salient features. We also study the model enriched with a short-range interaction and clarify the nature of the resulting ground state at low filling of holes and identify deconfined hole excitations near the hole filling $\nu^h=1/3$.