Matter-induced plaquette terms in a $\mathbb{Z}_2$ lattice gauge theory

TL;DR

This paper shows that dynamical matter in a $ ext{Z}_2$ lattice gauge theory naturally induces plaquette interactions, which are crucial for exotic phases, through numerical simulations of a coupled gauge-matter system.

Contribution

It demonstrates that matter fields can generate effective plaquette terms in a $ ext{Z}_2$ lattice gauge theory without explicit multi-body interactions, advancing understanding of topological quantum matter.

Findings

Large plaquette expectation values at small coupling and various fillings

Signatures of a confinement-deconfinement transition at weak coupling

Dynamical matter induces complex multi-body interactions

Abstract

Lattice gauge theories (LGTs) provide a powerful framework for studying confinement, topological order, and exotic quantum matter. In particular, the paradigmatic phenomenon of confinement, where dynamical matter is coupled to gauge fields and forms bound states, remains an open problem. In addition, LGTs can provide low-energy descriptions of quantum spin liquids, which is the focus of ongoing experimental research. However, the study of LGTs is often limited theoretically by their numerical complexity and experimentally in implementing challenging multi-body interactions, such as the plaquette terms crucial for the realization of many exotic phases of matter. Here we investigate a $(2+1)$D $\mathbb{Z}_2$ LGT coupled to hard-core bosonic matter featuring a global U(1) symmetry, and show that dynamical matter naturally induces sizable plaquette interactions even in the absence of explicit plaquette terms in the Hamiltonian. Using a combination of density matrix renormalization group simulations and neural quantum state calculations up to a system size of $20 \times 20$, we analyze the model across different fillings and electric field strengths. At small coupling strength, we find a large plaquette expectation value, independent of system size, for a wide range of fillings, which decreases in the presence of stronger electric fields. Furthermore, we observe signatures of a confinement-deconfinement transition at weak coupling strengths. Our results demonstrate that dynamical U(1) matter can induce complex multi-body interactions, suggesting a natural route to the realization of strong plaquette terms and paving the way for realizing a topological quantum spin liquid protected by a large gap.