Phase transitions of bosonic fractional quantum Hall effect in topological flat bands

TL;DR

This paper investigates phase transitions in bosonic fractional quantum Hall systems on topological flat bands, revealing continuous transitions to trivial insulators and a transition to superfluidity driven by interactions and periodic potentials.

Contribution

It demonstrates the nature of phase transitions in bosonic FQH states under varying potentials and interactions using advanced numerical methods.

Findings

Continuous transition from FQH liquid to Mott insulator with periodic potential.

Discontinuous transition from FQH liquid to superfluid as Hubbard repulsion decreases.

Energy and entanglement entropy show smooth crossover during the phase transition.

Abstract

We study the phase transitions of bosonic $\nu=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQH liquid would turn into a superfluid state with direct energy level crossing and a discontinuous leap of off-diagonal long-range order.