Phase diagram of generalized XY model using tensor renormalization group

TL;DR

This paper employs tensor renormalization group techniques to map out the phase diagram of a generalized XY model, revealing complex phase transitions including BKT and Ising types across various parameters.

Contribution

It introduces a comprehensive tensor network approach to analyze the phase structure of a generalized XY model with vortices, uncovering multiple transition lines and phases.

Findings

Identification of nematic, ferromagnetic, and disordered phases.

Observation of BKT-like and Ising-like transitions.

Mapping of the phase diagram over temperature and deformation parameters.

Abstract

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless (BKT) and Ising class. We explore the model for a wide range of temperatures, $T$, and the deformation parameter, $\Delta$, and compute specific heat along with integer and half-integer magnetic susceptibility, finding both BKT-like and Ising-like transitions and the region where they meet.