Berezinskii–Kosterlitz–Thouless Quantum Transition in Two Dimensions

TL;DR

This paper explores a quantum version of the BKT transition in two-dimensional systems, driven by topological defects like magnetic monopoles.

Contribution

The paper introduces a quantum BKT transition in 2D governed by an effective gauge field theory with a diverging dielectric constant.

Findings

Quantum BKT transitions can occur at zero temperature in 2D systems with a diverging dielectric constant.

Non-relativistic 2D magnetic monopoles induce quantum BKT transitions in compact U(1) gauge theories.

These transitions share the same diverging exponent z as quantum Griffiths transitions but are not disorder-related.

Abstract

The Berezinskii–Kosterlitz–Thouless (BKT) transition is the prototype of a phase transition driven by the formation and interaction of topological defects in two-dimensional (2D) systems. In typical models, these are vortices: above a transition temperature TBKT, vortices are free; below this transition temperature, they get confined. In this work, we extend the concept of BKT transition to quantum systems in two dimensions. In particular, we demonstrate that a zero-temperature quantum BKT phase transition driven by a coupling constant can occur in 2D models governed by an effective gauge field theory with a diverging dielectric constant. One particular example is that of a compact U(1) gauge theory with a diverging dielectric constant, where the quantum BKT transition is induced by non-relativistic, purely 2D magnetic monopoles, which can be viewed also as electric vortices. These quantum BKT transitions have the same diverging exponent z as the quantum Griffiths transition but are not related to disorder.