Shielding and localization in presence of long range hopping

TL;DR

This paper introduces the concept of Cooperative Shielding in quantum transport models with long-range hopping, revealing how it preserves localization and induces a gap, contrary to common expectations about long-range effects.

Contribution

It demonstrates that long-range hopping can induce a gap and shield excited states, maintaining localization even in strong long-range coupling regimes.

Findings

Long-range hopping induces a superconducting-like gap.

Shielding prevents long-range hopping from affecting excited states.

Localized features persist despite strong long-range interactions.

Abstract

We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited states can be induced, which is mathematically equivalent to the superconducting gap. In the gapped regime, the dynamics within the excited states subspace is shielded from long range hopping, namely it occurs as if long range hopping would be absent. This is a cooperative phenomenon since shielding is effective over a time scale which diverges with the system size. We named this effect {\it Cooperative Shielding}. We also discuss the consequences of our findings on Anderson localization. Long range hopping is usually thought to destroy localization due to the fact that it induces an infinite number of resonances. Contrary to this common lore we show that the excited states display strong localized features when shielding is effective even in the regime of strong long range coupling. A brief discussion on the extension of our results to generic power-law decaying long range hopping is also given. Our preliminary results confirms that the effects found for the infinite range case are generic.