Two interacting particles in a disordered chain IV: Scaling of level curvatures

TL;DR

This study numerically investigates how interactions affect the level curvatures of two particles in disordered rings, revealing that interactions modify these curvatures differently in localized and metallic regimes, following a conductance-like scaling.

Contribution

It demonstrates that interactions influence level curvatures in disordered systems and that these effects follow a universal scaling law, confirming previous theoretical predictions.

Findings

Interactions increase typical curvatures in localized regimes.

Interactions decrease typical curvatures in metallic regimes.

Curvature changes follow a single-parameter scaling law.

Abstract

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced changes of the typical curvatures at different energies and disorder strengths exhibit one-parameter scaling with a conductance-like single parameter. This suggests that interactions could influence the conductance of mesoscopic systems similarly.