Phase diagram of $\nu=\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings

TL;DR

This paper maps the phase diagram of a bilayer bosonic fractional quantum Hall system at total filling factor one, identifying conditions for Moore-Read, Halperin, and coupled Moore-Read phases driven by inter-layer interactions and tunneling.

Contribution

It provides the first detailed numerical phase diagram of the bilayer bosonic FQH system, highlighting the emergence of Moore-Read and other phases under various inter-layer couplings.

Findings

Moore-Read phase confirmed for both even and odd particle numbers.

Inter-layer interactions and tunneling can induce Moore-Read phase in the bilayer system.

The (220) Halperin and coupled Moore-Read states are also stabilized under certain conditions.

Abstract

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $\nu=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is $SU(2)$ symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.