Symmetry breaking at a topological phase transition

TL;DR

This paper introduces a broader concept of symmetry breaking at topological phase transitions, specifically the BKT transition, explaining how order parameter phase fluctuations behave and reconcile experimental observations with theoretical expectations.

Contribution

It develops the concept of general symmetry breaking, unifying spontaneous and topological symmetry breaking by analyzing phase fluctuation dynamics at the BKT transition.

Findings

Demonstrates slow directional mixing of the order parameter in the BKT phase

Shows the order parameter chooses a well-defined direction in the thermodynamic limit

Provides a model for symmetry breaking timescales in BKT systems

Abstract

Spontaneous symmetry breaking is a foundational concept in physics. In condensed matter, it characterizes conventional continuous phase transitions but is absent at topological phase transitions such as the Berezinskii-Kosterlitz-Thouless (BKT) transition - as in the BKT case the expected norm (i.e., the magnitude) of the $U(1)$ order parameter vanishes in the thermodynamic limit at all nonzero temperatures. Phenomena consistent with low-temperature broken symmetry have been observed, however, in many different BKT experiments. Examples include recent experiments on superconducting films and the seminal work on two-dimensional arrays of Josephson junctions. While the inaccessibility of the above thermodynamic limit partially explains this paradox in finite systems, the full dynamical framework of symmetry breaking at the BKT transition remains unresolved. Here we provide this by introducing the broader concept of general symmetry breaking. This encompasses both spontaneous symmetry breaking and the BKT case by allowing the expected norm of the order parameter to go to zero in the thermodynamic limit, provided its directional phase fluctuations are asymptotically smaller. We demonstrate this asymptotically slow directional mixing in the low-temperature BKT phase. This explicitly shows that the order parameter arbitrarily chooses some well-defined direction in the thermodynamic limit, predicting negligible phase fluctuations compared to the expected norm in arbitrarily large experimental BKT systems. Our results provide a model for directional mixing timescales across the diverse array of experimental BKT systems. We suggest various experiments.