# Study of counterintuitive transport properties in the Aubry-Andr\'e-Harper model via entanglement entropy and persistent current

## TL;DR

This study investigates the transport properties of the Aubry-André-Harper model, revealing how entanglement entropy and persistent current behave differently at various spectral sub-band structures, especially at specific Fermi levels.

## Contribution

It uncovers the relationship between spectral sub-band structure and transport properties, highlighting the sensitivity of many-particle measures to these features and their dependence on system size.

## Key findings

- Entanglement entropy is suppressed in band gaps even in delocalized phase.
- Persistent current vanishes at certain Fermi levels corresponding to band gaps.
- Discontinuous vs. continuous behavior of persistent current fluctuations distinguishes special fillings.

## Abstract

The single particle eigenstates of the Aubry-Andr\'e-Harper model are known to show a delocalization-localization transition at a finite strength of the quasi-periodic disorder. In this work, we point out that an intimate relationship exists between the sub-band structure of the spectrum and transport properties of the model. To capture the transport properties we have not only used a variety of single-particle measures like inverse participation ratio, and von Neumann entropy, but also many-particle measures such as persistent current and its variance, and many body entanglement entropy. The many-particle measures are very sensitive to the sub-band structure of the spectrum. Even in the delocalized phase, surprisingly the entanglement entropy is substantially suppressed when the Fermi level is in the band gaps whereas the persistent current is vanishingly small for the same locations of the Fermi level. The entanglement entropy seems to follow area-law exclusively for these special locations of Fermi level or filling fractions of free fermions. A study of the standard deviation of persistent current offers further distinguishing features for the special fillings. In the delocalized phase, the standard deviation vs. mean persistent current curves are discontinuous for the non-special values of filling fractions and continuous (closed) for the special values of filling fractions whereas in the localized phase, these curves become straight lines for both types of filling fractions. We have also discussed how the results depend on the system size. Our results, specially on the persistent current, can potentially be tested experimentally using the present day set-ups based on ultra-cold atoms.