Confinement Induced Frustration in a One-Dimensional $\mathbb{Z}_2$ Lattice Gauge Theory

TL;DR

This paper investigates a one-dimensional $ ext{Z}_2$ lattice gauge theory with dynamical charges and nearest-neighbor interactions, revealing a complex phase diagram including Mott insulators, confined meson liquids, and frustrated regimes, with implications for ultracold atom experiments.

Contribution

It provides a combined numerical and analytical study of a simple $ ext{Z}_2$ gauge model, uncovering new phases and the effects of local and non-local interactions.

Findings

Identification of a Mott insulating phase stabilized by NN interactions.

Discovery of a Luttinger liquid of confined mesons.

Revelation of a frustrated regime at phase boundaries.

Abstract

Coupling dynamical charges to gauge fields can result in highly non-local interactions with a linear confining potential. As a consequence, individual particles bind into mesons which, in one dimension, become the new constituents of emergent Luttinger liquids. Furthermore, at commensurate fillings, different Mott-insulating states can be stabilized by including nearest-neighbour (NN) interactions among charges. However, rich phase diagrams expected in such models have not been fully explored and still lack comprehensive theoretical explanation. Here, by combining numerical and analytical tools, we study a simple one-dimensional $\mathbb{Z}_2$ lattice gauge theory at half-filling, where U$(1)$ matter is coupled to gauge fields and interacts through NN repulsion. We uncover a rich phase diagram where the local NN interaction stabilizes a Mott state of individual charges (or partons) on the one hand, and a Luttinger liquid of confined mesons on the other. Furthermore, at the interface between these two phases, we uncover a highly frustrated regime arising due to the competition between the local NN repulsion and the non-local confining interactions, realizing a pre-formed parton plasma. Our work is motivated by the recent progress in ultracold atom experiments, where such simple model could be readily implemented. For this reason we calculate the static structure factor which we propose as a simple probe to explore the phase diagram in an experimental setup.