Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

TL;DR

This paper applies the density matrix renormalization group method to the 19-vertex model to study the Berezinskii-Kosterlitz-Thouless transition, achieving precise conformal anomaly estimates.

Contribution

The authors develop a classification-based reduction technique for the transfer matrix, enabling efficient DMRG analysis of the 19-vertex model's phase transition.

Findings

Estimated conformal anomaly c=1.006(1) at the transition point

Reduced matrix dimension significantly improves computational efficiency

Validated DMRG approach for vertex models with topological phase transitions

Abstract

We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.90.+m, 02.70.-c