Generalized BKT Transitions and Persistent Order on the Lattice

TL;DR

This paper explores generalized BKT transitions on lattices with a $ ext{Z}_W$ symmetry, revealing persistent order and novel phase boundaries through Monte Carlo simulations, extending understanding of vortex-driven phase transitions.

Contribution

It introduces a class of lattice models with $ ext{Z}_W$ symmetry exhibiting persistent order and mixed anomalies, and numerically investigates their phase structure.

Findings

Existence of a phase boundary between gapped ordered and gapless phases.

Persistent order persists at finite lattice spacing for $W>1$.

Modified Villain models exhibit novel vortex-related phenomena.

Abstract

The BKT transition in low-dimensional systems with a $U(1)$ global symmetry separates a gapless conformal phase from a trivially gapped, disordered phase, and is driven by vortex proliferation. Recent developments in modified Villain discretizations provide a class of lattice models which have a $\mathbb{Z}_W$ global symmetry that counts vortices mod W, mixed 't Hooft anomalies, and persistent order even at finite lattice spacing. While there is no fully-disordered phase (except in the original BKT limit $W=1$) there is still a phase boundary which separates gapped ordered phases from gapless phases. I'll describe a numerical Monte Carlo exploration of these phenomena.