Kosterlitz-Thouless transition of quantum XY model in two dimensions

TL;DR

This study uses quantum Monte Carlo simulations to precisely analyze the Kosterlitz-Thouless transition in the 2D quantum XY model, confirming the theory's validity and accurately estimating the critical temperature and helicity modulus.

Contribution

First precise Monte Carlo estimation of the helicity modulus and critical temperature for the 2D quantum XY model, validating the Kosterlitz-Thouless theory.

Findings

Critical temperature estimated as T_KT = 0.3427(2)J.

Helicity modulus fits Kosterlitz renormalization group scaling.

Validation of Kosterlitz-Thouless theory for the quantum XY model.

Abstract

The two-dimensional $S=1/2$ XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to $128 \times 128$ near and below the critical temperature. The critical temperature is estimated as $T_{\rm KT} = 0.3427(2)J$. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.