Exact Topological Flat Bands from Continuum Landau Levels

Abstract

We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple analytic descriptions. These provide a valuable tool for constructing exactly solvable models. We also implement a numerical algorithm for finding the most local Hamiltonian with a flat Landau level. We find intriguing structures in the spatial dependence of the matrix elements for this optimized model. The models we construct serve as foundations for numerical and experimental studies of topological systems, both non-interacting and interacting.

6 pages, 4 figures

References in corpus (5)

• Fractional quantum Hall states at zero magnetic field
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Momentum-space instantons and maximally localized flat-band topological Hamiltonians
• Generalizations of Perelomov's identity on the completeness of coherent states