Phases at finite winding number of an Abelian lattice gauge theory

TL;DR

This paper investigates the condensation of string-like excitations in an Abelian lattice gauge theory using numerical simulations, revealing ground states characterized by torelon condensation and their relation to plaquette properties.

Contribution

It provides the first numerical evidence of torelon condensation in a 2+1D U(1) lattice gauge theory using matrix product states.

Findings

Existence of ground states with string-like excitations

Identification of torelon condensation phenomena

Correlation between plaquette properties and condensation

Abstract

Pure gauge theories are rather different from theories with pure scalar and fermionic matter, especially in terms of the nature of excitations. For example, in scalar and fermionic theories, one can create ultra-local excitations. For a gauge theory, such excitations need to be closed loops that do not violate gauge invariance. In this proceedings, we present a study on the condensation phenomenon associated with the string-like excitations of an Abelian lattice gauge theory. These phenomena are studied through numerical simulations of a $U(1)$ quantum link model in 2+1 dimensions in a ladder geometry using matrix product states. In this proceedings, we show the existence of ground states characterized by the presence of such string-like excitations. These are caused due to the condensation of torelons. We also study the relationship between the properties of the plaquettes in the ground state and the presence of such condensation phenomenon.