Berezinskii-Kosterlitz-Thouless transitions in the six-state clock model

TL;DR

This paper extends the level spectroscopy method to analyze Berezinskii-Kosterlitz-Thouless transitions in the 2D six-state clock model, confirming analytical predictions and exploring excitation degeneracies.

Contribution

The authors adapt the level spectroscopy method for multi-degenerated cases and apply it to the 2D six-state clock model, providing precise numerical confirmation of theoretical results.

Findings

Confirmed the self-dual point matches analytical predictions.

Extended level spectroscopy to multi-degenerated systems.

Identified degeneracy of excitation states at the self-dual point.

Abstract

Classical 2D clock model is known to have a critical phase with Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty, one of the authors has proposed the method called level spectroscopy, which is based on the conformal field theory. We extend this method to the multi-degenerated case. As an example, we study the classical 2D 6-clock model which can be mapped to the quantum self-dual 1D 6-clock model. Additionally, we confirm that the self-dual point has a precise numerical agreement with the analytical result, and we argue the degeneracy of the excitation states at the self-dual point from the effective field theoretical point of view.