Delocalization of two interacting particles in the two-dimensional Harper model

TL;DR

This paper investigates how two interacting particles behave in a two-dimensional quasiperiodic Harper model, revealing anomalous subdiffusive spreading and contrasting it with one-dimensional cases and disordered potentials.

Contribution

It demonstrates that in 2D quasiperiodic Harper models, two particles exhibit delocalization with subdiffusive spreading, differing from 1D models and disordered systems, and finds no evidence of ballistic FIKS pairs.

Findings

Two interacting particles delocalize with subdiffusive spreading (b≈0.5).

Spreading is stronger than in correlated disorder potentials.

No signatures of ballistic FIKS pairs in 2D Harper model.

Abstract

We study the problem of two interacting particles in a two-dimensional quasiperiodic potential of the Harper model. We consider an amplitude of the quasiperiodic potential such that in absence of interactions all eigenstates are exponentially localized while the two interacting particles are delocalized showing anomalous subdiffusive spreading over the lattice with the spreading exponent $b \approx 0.5$ instead of a usual diffusion with $b=1$. This spreading is stronger than in the case of a correlated disorder potential with a one particle localization length as for the quasiperiodic potential. At the same time we do not find signatures of ballistic FIKS pairs existing for two interacting particles in the one-dimensional Harper model.