# Interlayer correlated fractional quantum Hall state in the {\nu} = 4/5 bilayer system

## TL;DR

This study uses exact diagonalization to uncover an interlayer-correlated fractional quantum Hall state at filling factor 4/5 in a bilayer system, revealing a novel Abelian phase with unique topological properties and phase transitions influenced by tunneling.

## Contribution

It identifies and characterizes a new interlayer-correlated fractional quantum Hall phase at 4/5 filling, including its topological structure and the effects of tunneling and symmetry.

## Key findings

- Discovery of an interlayer-correlated Abelian phase with five-fold degeneracy.
- Identification of a unique 4x4 K-matrix class describing this phase.
- Proposal of a phase diagram showing transitions driven by tunneling and layer separation.

## Abstract

We perform exact diagonalization studies for fractional quantum Hall states at filing factor 4/5 in a bilayer system, on a torus with various aspect ratios and angles. We find that in the absence of tunneling, two weakly coupled 2/5-layers undergo a phase transition into an interlayer-correlated regime, which is also Abelian with the five-fold degeneracy on the torus. In the limit of zero layer separation, this phase becomes a singlet in the pseudospin variable describing the layer degree-of-freedom. By studying the Chern-number matrix, we show that the K-matrix describing the interlayer-correlated regime requires matrix dimension larger than two and this regime is in particular not described by a Halperin state. A detailed analysis of possible 4 X 4 K-matrices having the requisite symmetries and quantum numbers shows that there is only one equivalence class of such matrices. A model wave function representing this universality class is constructed. The role of separate particle number conservation in both layers is discussed, and it is argued that this additional symmetry allows for the further distinction of two different symmetry protected Abelian phases in the interlayer correlated regime. Interlayer tunneling breaks this symmetry, and can drive the system into a single-layer regime when strong enough. A qualitative phase diagram in the tunneling-layer separation parameter space is proposed based on our numerical results.