Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect

Abstract

While the understanding of Abelian topological order is comprehensive, how to describe the internal correlation structure of non-Abelian states is still outstanding. Here, we propose a general scheme based on the many-body Chern number matrix to characterize the non-Abelian multicomponent fractional quantum Hall states at filling factions ν = 2k/(2kM + 3) (k, M ∈ Z). As a concrete example, we study the many-body ground states of two-component bosons in topological flat band models. Utilizing density-matrix renormalization group and exact diagonalization methods, we demonstrate the emergence of the non-Abelian spin-singlet fractional quantum Hall effect under three-body interaction at a total filling factor ν = 4/3 in the lowest Chern band, whose topological nature is classified by six-fold degenerate ground states and fractionally quantized Chern number matrix.