Random matrix model for quantum dots with interactions and the conductance peak spacing distribution

TL;DR

This paper introduces a random interaction matrix model (RIMM) to describe the crossover in conductance peak spacing distributions in chaotic quantum dots with interactions, showing universality and dependence on a single parameter.

Contribution

The paper develops a new RIMM for strongly interacting fermionic systems with chaotic single-particle dynamics, capturing the universal crossover behavior in quantum dot conductance peak spacings.

Findings

The crossover from Wigner-Dyson to Gaussian-like distribution is universal within the model.

The crossover depends on a single scaled fluctuation parameter.

Comparison with an Anderson model confirms the RIMM's predictions.

Abstract

We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe the crossover of the peak spacing distribution from a Wigner-Dyson to a Gaussian-like distribution. The crossover is universal within the random matrix model and is shown to depend on a single parameter: a scaled fluctuation width of the interaction matrix elements. The crossover observed in the RIMM is compared with the results of an Anderson model with Coulomb interactions.