# Vortex supersolid in the XY model with tunable vortex fugacity

## TL;DR

This paper explores how adding a potential term to the XY model influences vortex behavior, leading to new phases like vortex lattices and supersolids, and reveals complex phase transition phenomena.

## Contribution

It introduces a modified XY model with tunable vortex fugacity, revealing novel vortex phases and complex transition behaviors not seen in traditional models.

## Key findings

- Emergence of vortex-antivortex lattice and supersolid phases
- Identification of a tricritical point with multiple transition types
- Distinct phase diagram compared to Coulomb gas models

## Abstract

In this paper, we investigate the XY model in the presence of an additional potential term that independently tunes the vortex fugacity favouring their nucleation. By increasing the strength of this term and thereby the vortex chemical potential {\mu}, we observe significant changes in the phase diagram with the emergence of a normal vortex-antivortex lattice as well as a superconducting vortex-antivortex crystal (lattice supersolid) phase. We examine the transition lines between these two phases and the conventional non-crystalline one as a function of both the temperature and the chemical potential. Our findings suggest the possibility of a peculiar tricritical point where second-order, first-order, and infinite-order transition lines meet. We discuss the differences between the present phase diagram and previous results for two-dimensional Coulomb gas models. Our study provides important insights into the behaviour of the modified XY model and opens up new possibilities for investigating the underlying physics of unconventional phase transitions.