Confinement-Higgs and deconfinement-Higgs transitions in three-dimensional $Z(2)$ LGT

TL;DR

This paper investigates the phase structure of a 3D $Z(2)$ lattice gauge theory with Higgs fields using numerical simulations, identifying three distinct phases and employing novel order parameters and simulation techniques.

Contribution

It introduces and applies new order parameters, including the Greensite-Matsuyama overlap operator, to distinguish phases in the $Z(2)$ LGT and explores the Higgs phase as a glassy state.

Findings

Identification of three distinct phases in the model.

Validation of the Greensite-Matsuyama operator as an effective phase discriminator.

Observation of Higgs phase as a glassy state similar to spin-glasses.

Abstract

We re-examine by numerical simulation the phase structure of the three-dimensional Abelian lattice gauge theory (LGT) with $Z(2)$ gauge fields coupled to $Z(2)$-valued Higgs fields. Concretely, we explore two different order parameters which are able to distinguish the three phases of the theory: (i) the Fredenhagen-Marcu operator used to discriminate between deconfinement and confinement/Higgs phases and (ii) the Greensite-Matsuyama overlap operator proposed recently to distinguish confinement and Higgs phases. The latter operator is an analog of the overlap Edwards-Anderson order parameter for spin-glasses. According to it, the Higgs phase is realized as a glassy phase of the gauge system. For this reason standard tricks for simulations of spin-glass phases are utilized in this work, namely tempered Monte Carlo and averaging over replicas. In addition, we also present results for a certain definition of distance between Higgs field configurations. Finally, we calculate various gauge-invariant correlation functions in order to extract the corresponding masses.