Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

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

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

We investigate disordered one- and two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the 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.

Original languageEnglish (US)
Article number021106
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume77
Issue number2
DOIs
StatePublished - Feb 7 2008

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Quantum Entanglement
Quantum Chaos
Heisenberg Model
Entanglement
chaos
statistics
Integrability
matrix theory
Hilbert space
Statistics
Quantum Information
Random Matrix Theory
Pure State
eigenvectors
purity
energy spectra
Principal Components
Energy Spectrum
fermions
disorders

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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Quantum chaos, delocalization, and entanglement in disordered Heisenberg models. / Brown, Winton G.; Santos, Lea F.; Starling, David J.; Viola, Lorenza.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 77, No. 2, 021106, 07.02.2008.

Research output: Contribution to journalArticle

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