Vortex operator and BKT transition in Abelian duality

Abstract

We give a new simple derivation for the sine-Gordon description of BerezinskiiKosterlitz-Thouless(BKT) phase transition (is driven by vortices). Our derivation is simpler than traditional derivations. Besides, our derivation is a continuous field theoretic derivation by using path integration, different from the traditional derivations which are based on lattice theory or based on Coulomb gas model. Our new derivation rely on Abelian duality of two dimensional quantum field theory. By utilizing this duality in path integration, we find that the vortex configurations are naturally mapped to exponential operators in dual description, these operators are the vortex operators that can create vortices, the sine-Gordon description then naturally follows. Our method may be useful for the investigation to the BKT physics of superconductors.

Models for $d$ Wave Topological Superconductors and Quantum Anomalous Hall Effect with Arbitrary Large Chern Numbers

“…This indicates that under the replacement w → 1/w, our model (18) will become a new model (called the dual model. This duality is reminiscent of the Abelian duality of two dimensional quantum field [41].) that is describing the same topological phase.…”