Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles

TL;DR

This paper investigates the distribution of level spacings in embedded Gaussian orthogonal ensembles (GOE) for interacting fermion and boson systems, confirming that local fluctuations follow classical Gaussian ensemble predictions.

Contribution

It provides numerical validation that local level fluctuations in embedded ensembles match analytical results from a 3x3 random matrix model, strengthening the connection to classical Gaussian ensembles.

Findings

Numerical results agree with analytical expressions for level spacings.

Embedded ensembles exhibit local fluctuations consistent with Gaussian ensembles.

Study covers systems with and without spin degrees of freedom.

Abstract

The probability distribution of the closest neighbor and farther neighbor spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded GOE of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a $3 \times 3$ random matrix model and other related quantities by Srivastava et. al [{\it J. Phys. A: Math. Theor.} {\bf 52} 025101 (2019)]. This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.