Exact Topological Flat Bands from Continuum Landau Levels

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 co...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Dong, Junkai, Mueller, Erich
Format: Article
Language:English
Subjects:
Algorithms
Dependence
Foundation construction
Mathematical models
Numerical analysis
Topology
Wave functions
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1910.08429