Three-component fractional quantum Hall effect in topological flat bands

TL;DR

This paper investigates the emergence of three-component fractional quantum Hall states in topological flat bands, demonstrating their topological properties and potential for non-Abelian states through numerical methods.

Contribution

It introduces a topological characterization of three-component FQH states using the K matrix and explores their properties in lattice models with strong interactions.

Findings

Identification of three-component FQH states at filling ν=3/4

Robust ground state degeneracy and spectral gap observed

Topological characterization via K matrix established

Abstract

We study the many-body ground states of three-component quantum particles in two prototypical topological lattice models under strong intercomponent and intracomponent repulsions. At band filling $\nu=3/4$ for hardcore bosons, we demonstrate the emergence of three-component fractional quantum Hall (FQH) effect characterized by the $\mathbf{K}$ matrix, through exact diagonalization study of four-fold quasidegenerate ground states with a robust spectrum gap and the combined density-matrix renormalization group calculation of fractional drag charge pumping. Further we formulate the topological characterization of FQH states of three-component Bose-Fermi mixtures at various fillings by the $\mathbf{K}$ matrix. At last we discuss the possible generalization of our approach to identify non-Abelian three-component spin-singlet FQH states.