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

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.