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arXiv · 1901.08374

Fractional Chern Insulators in Singular Geometries

Ai-Lei He·Wei-Wei Luo·Yi-Fei Wang·Chang-De Gong
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Abstract

The fractional quantum anomalous Hall (FQAH) states or fractional Chern insulator (FCI) states have been studied on two-dimensional (2D) flat lattices with different boundary conditions. Here, we propose the geometry-dependent FCI/FQAH states that interacting particles are bounded on 2D singular lattices with arbitrary $n$-fold rotational symmetry. Based on the generalized Pauli principle, we construct trial wave functions for the singular-lattice FCI/FQAH states with the aid of an effective projection approach, and compare them with the exact diagonalization results. High wave-function overlaps show that the singular-lattice FCI/FQAH states are certainly related to the geometric factor $β$. More interestingly, we observe some exotic degeneracy sequences of edge excitations in these singular-lattice FCI/FQAH states, and provide an explanation that two branches of edge excitations mix together.

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Ai-Lei He, Wei-Wei Luo, Yi-Fei Wang, Chang-De Gong. 2019-01-24. Fractional Chern Insulators in Singular Geometries. https://doi.org/10.1103/physrevb.99.165105

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