Bosonic Integer Quantum Hall States without Landau Levels on Square Lattice

TL;DR

This paper demonstrates the existence of a bosonic integer quantum Hall state on a square lattice with staggered magnetic flux, combining analytical and numerical methods to reveal its topological properties and edge modes.

Contribution

It introduces a new lattice model for bosonic IQH states, analytically predicts their topological features, and numerically confirms quantized Hall conductance and edge modes.

Findings

Quantized Hall conductance of b2acb1 2

Presence of two counter-propagating gapless edge modes

Analytical and numerical evidence for a symmetry-protected topological phase

Abstract

We study an interacting two-component hard-core bosons on square lattice for which, in the presence of staggered magnetic flux, the ground state is a bosonic integer quantum Hall (BIQH) state. Using a coupled-wire bosonization approach, we analytically show this model exhibits a BIQH state at total charge half filling associated with a symmetry-protected topological phase under $U(1)$ charge conservation. These theoretical expectations are verified, using the infinite density matrix renormalization group method, by providing numerical evidences for: (i) a quantized Hall conductance $\sigma_{xy}=\pm2$, and (ii) two counter-propagating gapless edge modes. Our model is a bosonic cousin of the fermionic Haldane model and serves as an additional case of analogy between bosonic and fermionic quantum Hall states.