Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

TL;DR

This paper analytically confirms the existence of the bosonic integer quantum Hall state in a honeycomb lattice model of hard-core bosons using a coupled-wire approach, and explores phase transitions and potential fractional states.

Contribution

It combines bosonization and coupled-wire methods to analytically verify the BIQH phase and its stability, also predicting a fractional quantum Hall state at 1/6 filling.

Findings

Confirmation of BIQH state at half filling

Analysis of phase transition as a deconfined quantum critical point

Prediction of Halperin (221) fractional quantum Hall state

Abstract

We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the $U(1)$ particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunneling that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the (2+1)-dimensional $O(4)$ nonlinear sigma model with the topological $\theta$ term at $\theta=\pi$. Finally we predict a possible fractional quantum Hall state, the Halperin (221) state, at 1/6 filling.