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

TL;DR

This paper introduces a new method using the many-body Chern number matrix to characterize non-Abelian topological order in fractional quantum Hall states, demonstrated through numerical studies of two-component bosons.

Contribution

It proposes a novel scheme based on the Chern number matrix to identify non-Abelian topological phases, validated by numerical analysis of a specific two-component boson system.

Findings

Identification of non-Abelian spin-singlet fractional quantum Hall effect

Demonstration of six-fold degenerate ground states

Fractionally quantized Chern number matrix

Abstract

While the internal structure of Abelian topological order is well understood, how to characterize the non-Abelian topological order is an outstanding issue. We propose a distinctive scheme based on the many-body Chern number matrix to characterize non-Abelian multicomponent fractional quantum Hall states. As a concrete example, we study the many-body ground state of two-component bosons at the filling faction $\nu=4/3$ in topological flat band models. Utilizing density-matrix renormalization group and exact diagonalization calculations, we demonstrate the emergence of non-Abelian spin-singlet fractional quantum Hall effect under three-body interaction, whose topological nature is classified by six-fold degenerate ground states and a fractionally quantized Chern number matrix.