Entanglement and Localization of Wavefunctions

Giraud, Olivier; Georgeot, Bertrand; Martin, John P.

doi:10.1007/978-90-481-3120-4_5

Cited by 1 publication

(1 citation statement)

References 35 publications

(44 reference statements)

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“…While this qualitatively agrees with the observed behavior, due to the fact that all interaction terms in the Hamiltonian are of a two-body nature, the components of the eigenvectors tend to be Hamming-correlated, resulting in significant deviations from the predicted inverse scaling law, especially at small ξ c . This effect was recently independently confirmed by Giraud and coworkers [95].…”

Section: B Energy and Delocalization Dependencesupporting

confidence: 59%

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

et al. 2008

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We investigate disordered one-and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin-and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.

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Section: B Energy and Delocalization Dependencesupporting

confidence: 59%