$\mathbb{Z}_N$ lattice gauge theory in a ladder geometry

TL;DR

This paper explores $ Z_N$ lattice gauge theories in ladder geometries, revealing a rich phase diagram with a gapless Coulomb phase, a BKT transition, and a novel quadrupolar phase, relevant for quantum simulation experiments.

Contribution

It introduces a detailed analysis of $ Z_N$ gauge theories in ladder geometries, including phase diagram characterization and discovery of a new quadrupolar phase.

Findings

Extended gapless Coulomb phase for N≥5

BKT phase transition separating phases

Discovery of a novel quadrupolar region

Abstract

Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we investigate Hamiltonian lattice gauge theories defined in two-leg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local $\mathbb{Z}_N$ gauge symmetries. We study its phase diagram based on both an effective low-energy field theory and density matrix renormalization group simulations. For $N\ge 5$, an extended gapless Coulomb phase emerges, which is separated by a Berezinskii-Kosterlitz-Thouless phase transition from the surrounding gapped phase. Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.