Fractional Chern Insulators in Singular Geometries

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 $\beta$. 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.

arXiv comment9 pages, 7 figures

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Cited by in corpus (5)

• Quasicrystalline Chern Insulators
• Hyperbolic Fractional Chern insulators
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Gravitational Response of Topological Quantum States of Matter
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice