Exciton Condensation in Quantum Hall Bilayers at Total Filling $\nu_T=5$

TL;DR

This paper investigates phase transitions in quantum Hall bilayers at total filling factor 5, revealing a topological phase transition between an exciton superfluid state and a Moore-Read state through numerical analysis.

Contribution

It identifies a continuous topological phase transition in quantum Hall bilayers, connecting exciton superfluidity with Moore-Read states using exact diagonalization.

Findings

Existence of a critical layer distance $d_c$ separating two phases.

Smooth connection of the topological phase to Moore-Read states beyond $d_c$.

Evidence of a possible continuous topological phase transition.

Abstract

We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels with varying the layer distance. Based on numerical exact diagonalization on torus, we identify two distinct phases separated by a critical layer distance $d_c$. From $d_c$ to infinite layer distance, the topological phase is smoothly connected to a direct tensor product of two Moore-Read states, while the interlayer coherence emerges at $d<d_c$ characterized by the $xy$ easy-plane ferromagnetic energy spectra, gapless pseudospin excitations and the finite exciton superfluid stiffness, corresponding to the exciton superfluid state. More interestingly, the results of the ground state fidelity, the evolution of energy spectra, and the superfluid stiffness indicate a possible continuous transition. Theoretically it can be interpreted as a topological phase transition which simultaneously changes the topology of ground state and breaks symmetry, providing an interesting example of transitions beyond Landau paradigm.