Bulk-edge correspondence in fractional Chern insulators

Abstract

It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional quantum Hall states -- via generalization of a gauge-fixed Wannier-Qi construction in the cylinder geometry. Our setup offers a number of important advantages compared to the earlier exact diagonalization studies on a torus. Most notably, it gives access to edge states and to a single-cut orbital entanglement spectrum, hence to the physics of bulk-edge correspondence. It is also readily implemented in the state-of-the-art density matrix renormalisation group method that allows for numerical simulations of significantly larger systems. We demonstrate our general approach on examples of flat-band models on ruby and kagome lattices at bosonic filling fractions $\nu =1/2$ and $\nu =1$, which show the signatures of (non)-Abelian phases, and establish the correspondence between the physics of edge states and the entanglement in the bulk. Notably, we find that the non-Abelian $\nu =1$ phase can be stabilized by purely on-site interactions in the presence of a confining potential.

A study of fractional Chern insulators on cylinders using DMRG and exact diagonalization. 5 pages, 4 figures

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• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Density matrix renormalization group on a cylinder in mixed real and momentum space
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• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Entanglement Spectrum of Su-Schrieffer-Heeger-Hubbard Model
• Recent Developments in Fractional Chern Insulators
• Wigner crystallization in topological flat bands
• Characterization of quasiholes in fractional Chern insulators
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• Edge Excitations in Fractional Chern Insulators
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Fractional Chern Insulators in Singular Geometries
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• Bulk-Edge Correspondence in Fractional Quantum Hall States
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Investigating disordered many-body system with entanglement in momentum space
• Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems