Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice

TL;DR

This paper demonstrates the emergence of a two-component bosonic integer quantum Hall effect in a topological triangular lattice at specific filling, revealing topological order, edge states, and phase transitions through numerical methods.

Contribution

It provides the first numerical evidence of a two-component bosonic integer quantum Hall state with a specific topological matrix in a topological lattice model.

Findings

Observation of BIQH effect at two-thirds filling

Identification of topological degeneracy and quantized Chern numbers

Detection of a first-order transition to a solid phase

Abstract

We study the many-body ground states of two-component hardcore bosons in topological triangular lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, two-component bosonic integer quantum hall (BIQH) effect emerges with the associated $\mathbf{K}=\begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$ matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized topological Chern number matrix $\mathbf{C}=\mathbf{K}^{-1}$, and (iii) two counterpropagating edge branches. Moreover, with increasing nearest-neighbor repulsions, the ground state undergoes a first-order transition from a BIQH liquid to a commensurate solid order.