Exact Topological Flat Bands from Continuum Landau Levels

TL;DR

This paper develops a family of lattice Hamiltonians with exactly flat topological bands derived from continuum Landau levels, facilitating the study of topological phases in lattice systems.

Contribution

It introduces an infinite family of analytically described Hamiltonians with flat topological bands from Landau levels and provides a numerical method to optimize their locality.

Findings

Constructed Hamiltonians with flat topological bands from Landau levels.

Developed a numerical algorithm for localizing Hamiltonian matrix elements.

Discovered intriguing spatial structures in optimized Hamiltonians.

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.