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Bulk-edge correspondence in fractional Chern insulators

Zhao Liu, D. L. Kovrizhin, and Emil J. Bergholtz
Phys. Rev. B 88, 081106(R) – Published 26 August 2013

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 renormalization 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 ν=1/2 and ν=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 ν=1 phase can be stabilized by purely on-site interactions in the presence of a confining potential.

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  • Received 4 April 2013

DOI:https://doi.org/10.1103/PhysRevB.88.081106

©2013 American Physical Society

Authors & Affiliations

Zhao Liu1, D. L. Kovrizhin2,3,4, and Emil J. Bergholtz5

  • 1Beijing Computational Science Research Center, Beijing 100084, China
  • 2T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 3Imperial College London, London SW7 2AZ, United Kingdom
  • 4Russian Research Centre, Kurchatov Institute, 1 Kurchatov Square, 123098 Moscow, Russia
  • 5Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

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Issue

Vol. 88, Iss. 8 — 15 August 2013

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