Entanglement spectrum and Wannier center flow of the Hofstadter problem

Details Entanglement spectrum and Wannier center flow of the Hofstadter problem Entanglement spectrum and Wannier center flow of the Hofstadter problem

2012-01-03

arxiv.org/abs/1201.0733v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 11 figures

Scientific paper

We examine the quantum entanglement spectra and Wannier functions of the square lattice Hofstadter model. Consistent with previous work on entanglement spectra of topological band structures, we find that the entanglement levels exhibit a spectral flow similar to that of the full system's energy spectrum. With open boundary conditions, there are also discontinuities in the entanglement spectra associated with the passage of an edge state through the Fermi level. We show how the entanglement spectrum can be understood by examining the band projectors of the full system and their behavior under adiabatic pumping. In so doing we make connections with the original TKNN work on topological two-dimensional band structures and their Chern numbers. Finally we consider Wannier states and their adiabatic flows, and draw connections to the entanglement properties.

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