Bosonic Fractional Quantum Hall States on a Finite Cylinder

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.

9 pages, 8 figures

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• Long-lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: a Bosonic Kane-Mele Model Platform
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Exploring helical phases of matter in bosonic ladders
• Floquet engineering flat bands for bosonic fractional quantum Hall in small lattices
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Measurable fractional spin for quantum Hall quasiparticles on the disk
• Chiral Gravitons on the Lattice
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code