Two Interacting Electrons in a Quasiperiodic Chain

TL;DR

This paper investigates how on-site Hubbard interactions influence two-electron states in a quasiperiodic chain, revealing various pairing states and transport behaviors across different regimes.

Contribution

It introduces a numerical analysis of two-electron interactions in a quasiperiodic system, identifying resonance, extended, multifractal, and localized pairing states.

Findings

Resonance two-particle pairing states emerge starting from energy U.

Interaction-assisted extended and multifractal pairing states are observed in metallic and critical regimes.

Localized pairing states form in gaps and subbands, affecting transport properties.

Abstract

We study numerically the effect of on-site Hubbard interaction U between two electrons in the quasiperiodic Harper's equation. In the periodic chain limit by mapping the problem to that of one electron in two dimensions with a diagonal line of impurities of strength U we demonstrate a band of resonance two particle pairing states starting from E=U. In the ballistic (metallic) regime we show explicitly interaction-assisted extended pairing states and multifractal pairing states in the diffusive (critical) regime. We also obtain localized pairing states in the gaps and the created subband due to U, whose number increases when going to the localized regime, which are responsible for reducing the velocity and the diffusion coefficient in the qualitatively similar to the non-interacting case ballistic and diffusive dynamics. In the localized regime we find propagation enhancement for small U and stronger localization for larger U, as in disordered systems.