Creating a bosonic fractional quantum Hall state by pairing fermions

TL;DR

This study demonstrates a topological phase transition from a fermionic quantum Hall state to a bosonic Laughlin state on a lattice, induced by increasing attractive interactions between spin-1/2 fermions under a magnetic field.

Contribution

It provides numerical evidence of a transition from fermionic to bosonic quantum Hall states driven by on-site attractive interactions.

Findings

Observation of a twofold quasidegeneracy in the energy spectrum.

Identification of the bosonic Laughlin state via entanglement spectra.

Evidence of a topological phase transition at a critical interaction strength.

Abstract

We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the entanglement spectra shows that the gapped ground state is the bosonic $1/2$ Laughlin state. Our work therefore provides compelling evidence of a topological phase transition from the fermionic quantum Hall state at unity filling to the bosonic Laughlin state at a critical attraction strength.