# Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks

## TL;DR

This paper employs tensor-network methods, specifically uniform matrix product states with non-abelian symmetry, to accurately analyze the Kosterlitz-Thouless transition in the 2D XY model, capturing key universal and critical properties.

## Contribution

It introduces a tensor-network approach with non-abelian symmetry to study the Kosterlitz-Thouless transition, providing high-precision estimates of critical behavior.

## Key findings

- Universal drop in spin stiffness at critical point
- Exponential divergence of correlation length in high-temperature phase
- High-precision estimate of critical temperature

## Abstract

We apply variational tensor-network methods for simulating the Kosterlitz-Thouless phase transition in the classical two-dimensional XY model. In particular, using uniform matrix product states (MPS) with non-abelian O(2) symmetry, we compute the universal drop in the spin stiffness at the critical point. In the critical low-temperature regime, we focus on the MPS entanglement spectrum to characterize the Luttinger-liquid phase. In the high-temperature phase, we confirm the exponential divergence of the correlation length and estimate the critical temperature with high precision. Our MPS approach can be used to study generic two-dimensional phase transitions with continuous symmetries.