Distribution of level spacing ratios using one- plus two-body random matrix ensembles

• Published in: Pramāṇa Vol. 84; no. 2; pp. 309 - 316
• Main Author: CHAVDA, N D
• Format: Journal Article
• Language: English
• Published: India Springer India 01.02.2015
• Subjects: Astronomy; Astrophysics and Astroparticles; Observations and Techniques; Physics; Physics and Astronomy; 05.40.−a; EGOE(1 + 2); BEGOE(1 + 2); spacing distribution; 05.30.Jp; Poisson–GOE transition; 05.30.Fk; Random matrix ensembles; 05.45.Mt; embedded ensembles
• ISSN: 0304-4289; 0973-7111
• DOI: 10.1007/s12043-015-0933-8

Probability distribution ( P ( r )) of the level spacing ratios has been introduced recently and is used to investigate many-body localization as well as to quantify the distance from integrability on finite size lattices. In this paper, we study the distribution of the ratio of consecutive level spacings using one-body plus two-body random matrix ensembles for finite interacting many-fermion and many-boson systems. P ( r ) for these ensembles move steadily from the Poisson to the Gaussian orthogonal ensemble (GOE) form as the two-body interaction strength λ is varied. Other related quantities are also used in the analysis to obtain critical strength λ c for the transition. The λ c values deduced using the P ( r ) analysis are in good agreement with the results obtained using the nearest neighbour spacing distribution (NNSD) analysis.