DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model

TL;DR

This study uses DMRG to analyze the Berezinskii-Kosterlitz-Thouless transitions in the 2D five-state clock model, confirming universal behaviors and critical exponents through boundary condition manipulations.

Contribution

It provides the first detailed DMRG analysis of BKT transitions in the 5-state clock model, confirming universal helicity modulus values and critical scaling behaviors.

Findings

Helicity modulus scaling matches essential singularities with σ=1/2.

Universal helicity modulus values are confirmed in the thermodynamic limit.

Magnetization scaling at the low-temperature transition aligns with η=1/4.

Abstract

The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus $\Upsilon_2$ is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with $\sigma=1/2$ at the two transitions. The predicted universal values of $\Upsilon_2$ are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the high-temperature BKT transition, like the XY model, and shown to take a new universal value at the low-temperature one. Finally, the scaling behavior of magnetization at the low-temperature transition is compatible with $\eta=1/4$.