Topological phase transition in a two-species fermion system: Effects of a rotating trap potential or a synthetic gauge field

TL;DR

This paper numerically studies a two-species fermion system under rotation or synthetic gauge fields, revealing a continuous topological phase transition from a fermionic integer quantum Hall state to a bosonic fractional quantum Hall state, characterized by gap closing and edge spectrum changes.

Contribution

It demonstrates a novel quantum phase transition between distinct topological states in a two-species fermion system with interactions and external gauge fields, supported by numerical evidence.

Findings

Identified a continuous transition from fermionic IQH to bosonic FQH state.

Characterized the transition by bulk gap closing and edge spectrum changes.

Compared numerical results with field theoretical predictions.

Abstract

We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor $\nu_f = 2$. We show that the system undergoes a continuous quantum phase transition from a $\nu_f = 2$ fermionic integer quantum Hall state formed by atoms, to a $\nu_b = 1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field theoretical predictions, and the case of $p$-wave pairing.