# Braiding properties of worldline configurations in hardcore lattice bosons

## TL;DR

This paper investigates the topological braiding properties of worldline configurations in hardcore Bose-Hubbard models, revealing how different quantum phases exhibit distinct braiding probability distributions through Monte Carlo simulations.

## Contribution

It introduces a topological perspective on worldline configurations in hardcore bosons and analyzes their braiding properties across various quantum phases.

## Key findings

- Different quantum phases have distinct braiding probability distributions.
- Ground-states correspond to specific topological braiding structures.
- Monte Carlo methods effectively characterize braiding in these systems.

## Abstract

In this manuscript, we study braiding properties of worldline configurations for a variety of ground-states of hardcore Bose-Hubbard models in two dimensions. Configurations are collections of particle paths and result from the path-integral formulation of statistical mechanics. For hard-core bosons, configurations can be seen as geometric braids and therefore can be assigned a certain topological structure, i.e. a way to classify braiding events among worldlines. By means of Monte Carlo calculations, we study superfluid phase and a variety of insulating phases and observe that ground-states of different quantum phases correspond to different probability distributions of braiding properties.