Helicity modulus in the bilayer XY model by worm algorithm

TL;DR

This paper extends the worm algorithm to layered XY models to analyze the helicity modulus, enabling the study of phase transitions and topological order in bilayer systems.

Contribution

It introduces a method to evaluate the helicity modulus in layered XY models using an extended worm algorithm, facilitating phase diagram analysis.

Findings

Helicity modulus effectively characterizes phase transitions in bilayer XY models.

The extended worm algorithm accurately computes the helicity modulus in layered systems.

Phase diagrams as a function of temperature and inter-layer coupling are determined.

Abstract

The behaviour of the helicity modulus has been frequently employed to investigate the onset of the topological order characterizing the low-temperature phase of the two-dimensional XY-model. We here present how the analysis based on the use of this key quantity can be applied to the study of the properties of coupled layers. To this aim, we first discuss how to extend the popular worm algorithm to a layered sample, and in particular to the evaluation of the longitudinal helicity, that we introduce taking care of the fact that the virtual twist representing the elastic deformation one applies to properly define the helicity modulus can act on a single layer or on all of them. We then apply the method to investigate the bilayer XY-model, showing how the helicity modulus can be used to determine the phase diagram of the model as a function of temperature and inter-layer coupling strength