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

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.

7 pages, 6 figures

References in corpus (8)

• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Novel method distinguishing between competing topological orders
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Quantum Hall States in Rapidly Rotating Two-Component Bose Gases
• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States
• Non-Abelian spin singlet states of two-component Bose gases in artificial gauge fields
• Two-component quantum Hall effects in topological flat bands
• SU(N) fractional quantum Hall effects in topological flat bands

Cited by in corpus (6)

• Recent Developments in Fractional Chern Insulators
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Anomalous Bilayer Quantum Hall Effect
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Three-component fractional quantum Hall effect in topological flat bands