$SU(2)/Z_2$ symmetry of the BKT transition and twisted boundary conditio n

TL;DR

This paper explores the SU(2)/Z_2 symmetry in the BKT transition, utilizing twisted boundary conditions to improve the determination of the critical point, and applies the method to spin chains.

Contribution

It introduces a novel approach linking the BKT transition to SU(2) Wess-Zumino-Witten models using twisted boundary conditions for better critical point estimation.

Findings

Level crossing method enhances convergence to the critical point.

Application to S=1,2 spin chains verifies the method's efficiency.

Relates operator content of BKT transition to SU(2) WZW model.

Abstract

Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D sine-Gordon model, plays an important role in the low dimensional physics. We relate the operator content of the BKT transition to that of the SU(2) Wess-Zumino-Witten model, using twisted boundary conditions. With this method, in order to determine the BKT critical point, we can use the level crossing of the lower excitations than the periodic boundary case, thus the convergence to the transition point is highly improved. Then we verify the efficiency of this method by applying to the S=1,2 spin chains.