Localization‐delocalization transitions in bosonic random matrix ensembles

• Published in: Annalen der Physik Vol. 529; no. 7
• Main Authors: Chavda, N. D., Kota, V. K. B.
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.07.2017
• Subjects: Eigenvectors; Embedded Ensembles; Embedded systems; Energy levels; Entanglement; Entropy; Entropy (Information theory); Interacting Bosons; Localization; Markers; Mathematical analysis; Mathematical models; Matrices (mathematics); Strength Functions; Thermalization (energy absorption)
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/andp.201600287

Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one‐ plus two‐body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis, considered are bosonic EGOE(1+2) for two‐species boson systems with a fictitious (F) spin degree of freedom [called BEGOE(1+2)‐F]. Numerical calculations are carried out as a function of the two‐body interaction strength (λ). It is shown that, in the region (defined by λ>λc) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit‐Wigner to Gaussian transition for λ>λFk>λc. Further, analyzing information entropy and participation ratio, it is established that there is a region defined by λ∼λt where the system exhibits thermalization. The F‐spin dependence of the transition markers λFk and λt follow from the propagator for the spectral variances. These results, well tested near the center of the spectrum and extend to the region within ±2σ to ±3σ from the center (σ2 is the spectral variance), establish universality of the transitions generated by embedded ensembles. In the second analysis, entanglement entropy is studied for spin‐less BEGOE(1+2) ensemble and shown that the results generated are close to the recently reported results for a Bose‐Hubbard model. Universality of the localizaton‐delocalization transitions generated by embedded random interaction matrix ensembles is established by showing that the ensembles for two species boson systems with a fictitious spin‐1/2 degree of freedom, generate three transition markers. The third marker defines a region of thermalization. Also for the first time, the bipartite entanglement entropy is studied using embedded ensembles for spin‐less boson systems and shown that the results are close to those obtained recently using Bose‐Hubbard models.