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  • Editors' Suggestion
  • Letter

Topological triviality of flat Hamiltonians

Pratik Sathe1,2,3,* and Rahul Roy2,†

  • 1Theoretical Division, T-4, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
  • 2Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095, USA
  • 3Information Science and Technology Institute, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *Contact author: psathe@lanl.gov
  • †Contact author: rroy@physics.ucla.edu
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Phys. Rev. B 111, L041105 – Published 9 January, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L041105

Abstract

Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat, and topologically nontrivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. We demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance.

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Phys. Rev. B 111, L041105– Published 9 January, 2025
  • Received 2 March 2024
  • Revised 17 December 2024
  • Accepted 18 December 2024
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