Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model

TL;DR

This paper confirms the Kosterlitz-Thouless theory for the 2D quantum XY model by precisely estimating the helicity modulus using advanced Monte Carlo simulations, revealing a universal jump characterized by a logarithmic scaling form.

Contribution

The study provides the first precise Monte Carlo estimates of the helicity modulus for the 2D quantum XY model, validating the universal jump predicted by the Kosterlitz-Thouless theory.

Findings

Helicity modulus fits a logarithmic scaling form

Universal jump in helicity modulus confirmed

Validation of Kosterlitz-Thouless theory for the model

Abstract

The helicity modulus of the S=1/2 XY model is precisely estimated through a world line quantum Monte Carlo method enhanced by a cluster update algorithm. The obtained estimates for various system sizes and temperatures are well fitted by a scaling form with L replaced by \log(L/L_0), which is inferred from the solution of the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.