Average-fluctuations separation in energy levels in dense interacting Boson systems

Patel, Kinnary; Desai, M.N.; Potbhare, V.; Kota, V. K. B.

doi:10.1016/s0375-9601(00)00605-8

Cited by 37 publications

(57 citation statements)

References 32 publications

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“…The construction of linearly independent eigenvectors C (sa) proceeds as for Fermions (see Ref. [32] for details), and one finds that these eigenvectors posses the same eigenvalues (14). As in the Fermionic case, the eigenvectors do not depend upon the rank k of the interaction, only the eigenvalues do.…”

Section: Eigenvector Expansion Of the Second Momentmentioning

confidence: 98%

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

et al. 2002

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We consider m spinless Bosons distributed over l degenerate singleparticle states and interacting through a k-body random interaction with Gaussian probability distribution (the Bosonic embedded k-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as l → ∞ or as m → ∞. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit l → ∞ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as m → ∞ with both k and l fixed. Here we show that the ensemble is not ergodic, and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency towards * Present address:

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Section: Eigenvector Expansion Of the Second Momentmentioning

confidence: 98%

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

et al. 2002

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“…For bosonic systems, embedded Gaussian orthogonal ensembles of one‐ plus two‐body interactions [denoted by BEGOE(1+2)] for finite isolated interacting spin‐less many‐boson systems have been analyzed in detail , as they are generic models for finite isolated interacting many‐boson systems. For m bosons in N single particle (sp) states, in addition to the dilute limit (defined by

m \to \infty

N \to \infty

m / N \to 0

), another limiting situation, namely the dense limit (defined by

m \to \infty

N \to \infty

m / N \to \infty

) is also possible.…”

Section: Introductionmentioning

confidence: 99%

Localization‐delocalization transitions in bosonic random matrix ensembles

Chavda

Kota

2017

Annalen der Physik

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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 > λ c ) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit-Wigner to Gaussian transition for λ > λ F k > λ c . Further, analyzing information entropy and participation ratio, it is established that there is a region defined by λ ∼ λ t where the system exhibits thermalization. The F -spin dependence of the transition markers λ F k and λ t 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 (σ 2 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.

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“…(2). We have considered a 100-member The nearest neighbor spacing distribution (NNSD), which gives information about level repulsion, is of GOE type for spin-less BEGOE(2) [1] and BEGOE(2)-F [6]. In Fig.…”

Section: Results For Spectral Properties: Propagation Of Energy Cmentioning

confidence: 99%

“…The NNSDs are obtained by unfolding each spectrum in the ensemble, using the method described in [1], with the smooth density as a corrected Gaussian with corrections involving up to 6th order moments of the density function. In the calculations, 80% of the eigenvalues (dropping 10% from both ends of the spectrum) from each member are employed.…”

Section: Results For Spectral Properties: Propagation Of Energy Cmentioning

confidence: 99%

Random matrix ensemble with random two-body interactions in the presence of a mean field for spin-one boson systems

et al. 2013

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For m number of bosons, carrying spin (S=1) degree of freedom, in Ω number of single particle orbitals, each triply degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by random two-body interactions that are spin (S) scalar [BEGOE(2)-S1]. The embedding algebra is U (3) ⊃ G ⊃ G1 ⊗ SO(3) with SO(3) generating spin S. A method for constructing the ensembles in fixed-(m, S) space has been developed. Numerical calculations show that the form of the fixed-(m, S) density of states is close to Gaussian and level fluctuations follow GOE. Propagation formulas for the fixed-(m, S) space energy centroids and spectral variances are derived for a general one plus two-body Hamiltonian preserving spin. In addition to these, we also introduce two different pairing symmetry algebras in the space defined by BEGOE(2)-S1 and the structure of ground states is studied for each paring symmetry.

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Average-fluctuations separation in energy levels in dense interacting Boson systems

Cited by 37 publications

References 32 publications

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

Localization‐delocalization transitions in bosonic random matrix ensembles

Random matrix ensemble with random two-body interactions in the presence of a mean field for spin-one boson systems

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