Fractional quantum Hall effect of Bose-Fermi mixtures

TL;DR

This paper theoretically demonstrates a fractional quantum Hall effect in Bose-Fermi mixtures with novel topological orders, characterized by a specific K-matrix, using advanced numerical methods and topological analysis.

Contribution

It introduces a new class of fractional quantum Hall states in Bose-Fermi mixtures classified by a specific K-matrix, expanding the understanding of topological orders in multicomponent systems.

Findings

Topological ground-state degeneracy matches the K-matrix determinant.

Fractionally quantized Chern number matrix aligns with the inverse of the K-matrix.

Edge states exhibit two chiral branches with level counting consistent with conformal field theory.

Abstract

Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of strongly correlated Bose-Fermi mixtures classified by the $\mathbf{K}=\begin{pmatrix} m & 1\\ 1 & n\\ \end{pmatrix}$ matrix (even $m$ for boson and odd $n$ for fermion), using topological flat band models. Utilizing the state-of-the-art exact diagonalization and density-matrix renormalization group methods, we build up the topological characterization based on three inherent aspects: (i) topological $(mn-1)$-fold ground-state degeneracy equivalent to the determinant of the $\mathbf{K}$ matrix, (ii) fractionally quantized topological Chern number matrix equivalent to the inverse of the $\mathbf{K}$ matrix, and (iii) two parallel-propagating chiral edge branches with level counting $1,2,5,10$ consistent with the conformal field theory description.