Unbinding of giant vortices in states of competing order

TL;DR

This paper investigates how vortices in a two-dimensional system with competing orders unbind as the system approaches a high-symmetry point, revealing diverging core sizes and vanishing transition temperatures.

Contribution

The study introduces a variational and renormalization group analysis showing vortex core divergence and symmetry restoration near a high-symmetry point in systems with competing orders.

Findings

Vortex core size diverges as 1/√Δ near the high-symmetry point.

BKT transition temperature vanishes as 1/ln(1/Δ).

Full symmetry is restored within vortex cores.

Abstract

We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O($M$), near a point in parameter space where they couple to become a single O($2+M$) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as $1/\sqrt{\Delta}$ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as $1/\ln(1/\Delta)$, where $\Delta$ denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.