# Bosonic Fractional Quantum Hall States on a Finite Cylinder

## TL;DR

This paper studies bosonic fractional quantum Hall states on a finite cylindrical lattice, demonstrating topological order and Laughlin-like behavior through entanglement entropy, density profiles, and edge currents, and analyzing how these features depend on magnetic flux and interactions.

## Contribution

It provides the first detailed numerical analysis of bosonic FQH states on a finite cylinder, showing topological order and phase transitions influenced by flux density and interactions.

## Key findings

- Supports topologically ordered states with entanglement entropy matching Laughlin state
- Shows signatures of fractional quantum Hall states in density and current profiles
- Reveals phase transition behaviors depending on magnetic flux and interaction strength

## Abstract

We investigate the ground state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction $\nu=1/2$. We find that our system supports topologically ordered states by calculating the topological entanglement entropy, and its value is in good agreement with the theoretical value for the $\nu=1/2$ Laughlin state. By exploring the behaviour of the density profiles, edge currents and single-particle correlation functions, we find that the ground state on the cylinder shows all signatures of a fractional quantum Hall state even for large values of the magnetic flux density. Furthermore, we determine the dependence of the correlation functions and edge currents on the interaction strength. We find that depending on the magnetic flux density, the transition towards Laughlin-like behaviour can be either smooth or happens abruptly for some critical interaction strength.