Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

Brown, Winton G.; Santos, Lea F.; Starling, David J.; Viola, Lorenza

doi:10.1103/physreve.77.021106

Cited by 70 publications

(59 citation statements)

References 98 publications

(173 reference statements)

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“…The entanglement measures, introduced in the context of Quantum Information Science, are used to characterize complexity in quantum many‐body systems. Entanglement and delocalization are found to be strongly correlated for disordered spin‐1/2 lattice systems .…”

Section: Thermodynamic Region: λT Markermentioning

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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Section: Thermodynamic Region: λT Markermentioning

confidence: 99%

Localization‐delocalization transitions in bosonic random matrix ensembles

Chavda

Kota

2017

Annalen der Physik

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“…Our analysis is thus restricted to a particular S z tot -sector. In order to deal with a reasonably large subspace, other symmetries [20] are avoided as follows. Open boundary conditions prevent momentum conservation; μ = 1 avoid conservation of total spin; and the subspace with L/3 up-spins guarantee that S z tot = 0.…”

Section: Models and Quenchesmentioning

confidence: 99%

Isolated many-body quantum systems far from equilibrium: Relaxation process and thermalization

Torres-Herrera

Santos

2014

AIP Conference Proceedings

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Equilibration of an isolated quantum many-body system Phys. Today Abstract. We present an overview of our recent numerical and analytical results on the dynamics of isolated interacting quantum systems that are taken far from equilibrium by an abrupt perturbation. The studies are carried out on one-dimensional systems of spins-1/2, which are paradigmatic models of many-body quantum systems. Our results show the role of the interplay between the initial state and the post-perturbation Hamiltonian in the relaxation process, the size of the fluctuations after equilibration, and the viability of thermalization.

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“…x σ (2) x , and σ (1) y σ (2) y . The trace and trace-norm of the projection of each operator into S 0 may be found using combinatorial arguments presented in [40], yielding: tr(Πσ (1) z Π) = tr(Πσ (2) z Π) = 0, tr((Πσ…”

Section: Average Generalized Entanglement Of Random Pure Statesmentioning

confidence: 99%

Generalized entanglement as a framework for complex quantum systems: purity versus delocalization measures

Viola¹,

Brown²

2007

J. Phys. A: Math. Theor.

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We establish contact between the delocalization properties of pure quantum states, as quantified by their number of principal components, and the average generalized entanglement properties, as quantified by purity measures relative to different observable sets. We find that correlations between products of state vector components with respect to Hamming distance play an important role in the structure of subsystem-based purity measures. In particular, we derive general conditions under which the amount of global multipartite entanglement relates to the inverse participation ratio averaged over a maximal set of mutually unbiased product bases. Furthermore, we provide a method for computing the expected amount of generalized entanglement with respect to an arbitrary observable set for random pure states. Specific examples and an explicit application to a disordered quantum spin chain are discussed.

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Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

Cited by 70 publications

References 98 publications

Localization‐delocalization transitions in bosonic random matrix ensembles

Localization‐delocalization transitions in bosonic random matrix ensembles

Isolated many-body quantum systems far from equilibrium: Relaxation process and thermalization

Generalized entanglement as a framework for complex quantum systems: purity versus delocalization measures

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