Defect mediated melting and the breaking of quantum double symmetries

TL;DR

This paper develops a formalism based on breaking quantum double symmetries to classify defect-mediated melting processes, revealing how symmetry breaking and restoration govern phase transitions in various systems.

Contribution

It introduces a systematic approach to classify defect condensates and analyze symmetry breaking/restoration in melting phenomena using quantum double symmetry formalism.

Findings

Rephrases known Abelian defect condensate cases like Kosterlitz-Thouless transition.

Analyzes non-Abelian case of hexagonal crystal and hexatic phase formation.

Describes possible phases and symmetry behaviors in defect-mediated melting.

Abstract

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.