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Bulletin of the American Physical Society

The Fractional Quantum Hall States at $\nu=13/5$ and $12/5$ and their Non-Abelian Nature

Wenguang Zhu, Shou-Shu Gong, D. N. Sheng

Published Mar 16, 2016• 0 citations
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The Fractional Quantum Hall States at ν=13/5\nu=13/5ν=13/5 and 12/512/512/5 and their Non-Abelian Nature
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 $\ensuremath{\nu}=4/3$ 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 sixfold degenerate ground states and a fractionally quantized Chern-number matrix.