BKT phase transitions in two-dimensional systems with internal symmetries

TL;DR

This paper investigates BKT phase transitions in 2D systems with internal abelian symmetries, identifying conditions for their occurrence and analyzing their critical properties through effective field theories related to conformal field theories.

Contribution

It derives effective actions for 2D chiral models on maximal abelian tori and links their critical behavior to Coxeter numbers and conformal field theories with integer central charge.

Findings

BKT transitions require conformal invariance and abelian vacuum manifold topology.

Effective theories are characterized by Coxeter numbers and conformal field theory properties.

Full symmetry restoration in massive phases is discussed.

Abstract

The Berezinsky-Kosterlitz-Thouless (BKT) type phase transitions in two-dimensional systems with internal abelian continuous symmetries are investigated. The necessary conditions for they can take place are: 1) conformal invariance of the kinetic part of the model action, 2) vacuum manifold must be degenerated with abelian discrete homotopy group pi_1. Then topological excitations have a logarithmically divergent energy and they can be described by effective field theories generalizing the two-dimensional euclidean sine-Gordon theory, which is an effective theory of the initial XY-model. In particular, the effective actions for the two-dimensional chiral models on maximal abelian tori T_G of simple compact groups G are found. Critical properties of possible effective theories are determined and it is shown that they are characterized by the Coxeter number h_G of lattices from the series A,D,E,Z and can be interpreted as those of conformal field theories with integer central charge C=n, where n is a rank of the groups pi_1 and G. A possibility of restoration of full symmetry group G in massive phase is also dicussed.