Entanglement spectrum and Wannier center flow of the Hofstadter problem

Understand

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.
• While the energy spectra are continuous, with open boundary conditions the entanglement spectra exhibit discontinuities associated with the passage of an energy 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.