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

Abstract

We investigate the interplay of quantum one-dimensional discrete Z2 gauge fields and fermion matter with emphasis on fractionalized fermionic hole excitations whose deconfined nature we elucidate. 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 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.

Confinement induced frustration in a one-dimensional Z2 lattice gauge theory

“…Previous theoretical studies of the system we consider focused on liquid phases at generic fillings and without the NN repulsion [25], near-full filling [26], and it has been shown that the NN repulsion leads to mesonic Mott insulating states at two-thirds filling [27]. At this commensurate filling, n = 2/3, the gauge-mediated confining potential and the NN repulsion act in concert without creating frustration, which results in a phase diagram with three different regimes: deconfined partons in the absence of the confining field, dimers (mesons) consisting of pairs of confined partons [25], and a Mott state of crystallized dimers [27].…”