Single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus

Cécile Repellin, Titus Neupert, Zlatko Papić, and Nicolas Regnault
Phys. Rev. B 90, 045114 – Published 15 July 2014

Abstract

We analyze the collective magnetoroton excitations of bosonic Laughlin ν=12 fractional quantum Hall (FQH) states on the torus and of their analog on the lattice, the fractional Chern insulators (FCIs). We show that, by applying the appropriate mapping of momentum quantum numbers between the two systems, the magnetoroton mode can be identified in FCIs and that it contains the same number of states as in the FQH case. Further, we numerically test the single-mode approximation to the magnetoroton mode for both the FQH and FCI cases. This proves particularly challenging for the FCI because its eigenstates have a lower translational symmetry than the FQH states. In spite of this, we construct the FCI single-mode approximation such that it carries the same momenta as the FQH states, allowing for a direct comparison between the two systems. We show that the single-mode approximation captures well a dispersive subset of the magnetoroton excitations both for the FQH and the FCI cases. We find remarkable quantitative agreement between the two systems. For example, the many-body excitation gap extrapolates to almost the same value in the thermodynamic limit.

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  • Received 25 April 2014
  • Revised 2 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.045114

©2014 American Physical Society

Authors & Affiliations

Cécile Repellin1, Titus Neupert2, Zlatko Papić3,4, and Nicolas Regnault5,1

  • 1Laboratoire Pierre Aigrain, ENS-CNRS UMR 8551, Universités P. et M. Curie and Paris-Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France
  • 2Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
  • 4Institute for Quantum Computing, Waterloo, Ontario, Canada N2L 3G1
  • 5Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 90, Iss. 4 — 15 July 2014

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