Density matrix renormalization group for 19-vertex model

TL;DR

This paper applies the density matrix renormalization group method to the 19-vertex model, efficiently reducing transfer matrix dimensions and accurately determining the conformal anomaly near the Kosterlitz-Thouless transition.

Contribution

It introduces a novel application of the DMRG method to the 19-vertex model, leveraging symmetry properties to improve computational efficiency and accuracy.

Findings

Accurate conformal anomaly value near the BKT transition

Effective reduction of transfer matrix dimension

Validation of the 19-vertex model's relation to the XY model

Abstract

We embody the density matrix renormalization group method for the 19-vertex model on a square lattice; the 19-vertex model is regarded to be equivalent to the XY model for small interaction. The transfer matrix of the 19-vertex model is classified by the total number of arrows incoming into one layer of the lattice. By using this property, we reduce the dimension of the transfer matrix appearing in the density matrix renormalizaion group method and obtain a very nice value of the conformal anomaly which is consistent with the value at the Berezinskii-Kosterlitz-Thouless transition point. Keyword : Kosterlitz-Thouless, Renormalization group