Two interacting particles at the metal-insulator transition

TL;DR

This study examines how electronic interactions influence the metal-insulator transition in a quasiperiodic 1D system, finding that short-range interactions localize some states but do not alter the transition point, while long-range interactions shift the transition.

Contribution

It provides new insights into the effects of Hubbard and long-range interactions on the MIT in the Aubry-André model, showing that the transition remains robust against short-range interactions.

Findings

Interaction localizes some states in the metallic phase.

MIT remains unaffected by Hubbard interaction.

Long-range interactions shift the transition to smaller potential strengths.

Abstract

To investigate the influence of electronic interaction on the metal-insulator transition (MIT), we consider the Aubry-Andr\'{e} (or Harper) model which describes a quasiperiodic one-dimensional quantum system of non-interacting electrons and exhibits an MIT. For a two-particle system, we study the effect of a Hubbard interaction on the transition by means of the transfer-matrix method and finite-size scaling. In agreement with previous studies we find that the interaction localizes some states in the otherwise metallic phase of the system. Nevertheless, the MIT remains unaffected by the interaction. For a long-range interaction, many more states become localized for sufficiently large interaction strength and the MIT appears to shift towards smaller quasiperiodic potential strength.