Phase diagram ofν=12+12bilayer bosons with interlayer couplings

Abstract

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor ν = 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.

Emergent particle-hole symmetry in spinful bosonic quantum Hall systems

“…For example, we can add some V 1 pseudo-potential as an additional knob while preserving the SU (2) symmetry. For ν = 1 [80] and ν = 4/3 (see Appendix C), the previous description holds true for V 1 0.3 beyond which the system spontaneously fully polarizes. From our exact diagonalization on both the sphere and the torus geometries, the only option for a would be a narrow region close to the transition toward the fully polarized regime.…”

“…In particular, the transition to a fully polarized state occurs around V 1 0.4 irrespective of the shift. This value of V 1 also leads to the system full polarization for ν = 1 [80] For spinless fermions, the particle-hole symmetry is valid for the whole spectrum. This implies that the gaps (both charge and neutral) are identical.…”

“…For spinless bosons, previous studies [30,[80][81][82][83][84][85] have shown strong evidence that the two-body hardcore interaction leads to an emerging Moore-Read state. Among the other possible phases are two decoupled copies of the Laughlin ν = 1/2 state (i.e., the Halperin (220) state) or the coupled Moore-Read state [86].…”

“…The phase diagram of interacting bosons at filling factor ν = 1 hosts a large variety of phases [39,80] depending on the interaction. For spinless bosons, previous studies [30,[80][81][82][83][84][85] have shown strong evidence that the two-body hardcore interaction leads to an emerging Moore-Read state.…”

Variational Ansatz for an Abelian to Non-Abelian Topological Phase Transition in ν=1/2+1/2 Bilayers

“…It has a four-fold topological degeneracy on the torus, corresponding to the four anyons of the underlying Abelian topological order [40]. Under the global layer permutation P z (swapping ↑ and ↓) which com-mutes with H int , three of them are even while the last one is odd [68]. Coupling of the two layers is achieved by introducing tunneling as H tun = −JtS x .…”