Probability Distribution of the Ratio of Consecutive Level Spacings in Interacting Particle Systems

TL;DR

This paper investigates the probability distribution of ratios of consecutive level spacings in interacting particle systems, confirming that local level fluctuations follow classical Gaussian ensemble predictions.

Contribution

It provides numerical validation that embedded ensembles' local level fluctuations align with Gaussian ensemble results across various particle systems.

Findings

Numerical results closely match the analytic distribution form.

Local level fluctuations follow Gaussian ensemble predictions.

Results hold for systems with and without spin, fermions and bosons.

Abstract

We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between the numerical results and the recently derived analytic form for the distribution and other related quantities is found to be close. This establishes conclusively that local level fluctuations generated by embedded ensembles follow the results of classical Gaussian ensembles.