Flat bands and entanglement in the Kitaev ladder

TL;DR

This paper discovers flat bands and localized states in a Kitaev ladder, revealing their topological properties and phase transitions through entanglement entropy analysis, with implications for understanding quantum localization and topological phases.

Contribution

It identifies conditions for flat bands in a Kitaev ladder and maps it to an interlinked lattice, providing new insights into topological phase transitions via entanglement entropy.

Findings

Flat bands exist under specific parameters.

Localized eigenstates are compact and cover two unit cells.

Entanglement entropy features correlate with band crossings.

Abstract

We report the existence of \emph{flat bands} in a p-wave superconducting Kitaev ladder. We identify two sets of parameters for which the Kitaev ladder sustains flat bands. These flat bands are accompanied by highly localized eigenstates known as compact localized states. Invoking a Bogoliubov transformation, the Kitaev ladder can be mapped into an interlinked cross-stitch lattice. The mapping helps to reveal the compactness of the eigenstates each of which covers only two unit cells of the interlinked cross-stitch lattice. The Kitaev Hamiltonian undergoes a topological-to-trivial phase transition when certain parameters are fine-tuned. Correlation matrix techniques allow us to compute entanglement entropy of the many-body eigenstates. The study of entanglement entropy affords fresh insight into the topological phase transitions in the model. Sharp features in entanglement entropy when bands cross indicate a deep underlying relationship between entanglement entropy and dispersion.