Correlation functions of the 2D sine-Gordon model

TL;DR

This paper investigates the correlation functions of the 2D sine-Gordon model, especially near the BKT transition, using real-space renormalization to accurately identify the critical line and reveal new universal relations.

Contribution

The study introduces a method to determine the BKT transition point precisely from small system sizes by analyzing eigenvalue degeneracies, and uncovers a new universal relation linking Abelian and non-Abelian bosonization.

Findings

Eigenvalues become degenerate on the BKT line, including logarithmic corrections.

The degeneracy allows high-precision determination of the BKT critical line.

A new universal relation between Abelian and non-Abelian bosonization is discovered.

Abstract

A number of two-dimensional(2D) critical phenomena can be described in terms of the 2D sine-Gordon model. With the bosonization, several 1D quantum systems are also transformed to the same model. However, the transition of the 2D sine-Gordon model, Berezinskii-Kosterlitz-Thouless(BKT) transition, is essentially different from the second-order transition. The divergence of the correlation length is more rapid than any power-law, and there are logarithmic corrections. These pathological features make difficult to determine the BKT transition point and critical indices from finite-size calculations. In this paper, we calculate the several correlation functions of this model using a real-space renormalization technique. It is found that the several correlation functions, or eigenvalues of the corresponding transfer matrix for a finite system, become degenerate on the BKT line including logarithmic corrections. By the use of this degeneracy, which reflects the hidden SU(2) symmetry on the BKT line,it is possible to determine the BKT critical line with high precision from small size data, and to identify the universality class. In addition, a new universal relation is found. This reveals the relation between the Abelian and the non-Abelian bosonization.