Level curvatures, spectral statistics and scaling for interacting particles

TL;DR

This paper investigates how interactions between two particles in a random potential affect their spectral properties and mobility, revealing different behaviors in metals and insulators and introducing a new spectral curvature concept.

Contribution

It introduces a novel curvature measure of topological origin that characterizes the universal spectral rigidity scale in interacting particle systems.

Findings

Interaction decreases mobility in metals

Interaction increases mobility in insulators

A new topological curvature defines the universal spectral rigidity scale

Abstract

The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock states is shown to decrease the mobility in metals and to increase it in insulators. In contrast to the single particle case, the spectral rigidity is not directly related to the level curvature. Therefore, another curvature of topological origin is introduced, which defines the energy scale below which the spectrum has the universal Wigner-Dyson rigidity.