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  Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum

Tomsovic, S., Lakshminarayan, A., Srivastava, S. C. L., & Bäcker, A. (2018). Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum. Physical Review E, 98(3): 032209. doi:10.1103/PhysRevE.98.032209.

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Tomsovic, Steven1, Author           
Lakshminarayan, Arul1, Author           
Srivastava, Shashi Chandra Lal1, Author           
Bäcker, Arnd1, Author           
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1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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 MPIPKS: Semiclassics and chaos in quantum systems
 Abstract: We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the entanglement expected of fully randomized states in the opposite limit is governed by the single scaling transition parameter Lambda. The behaviors apply equally well to few- and many-body systems, e.g., interacting particles in quantum dots, spin chains, coupled quantum maps, and Floquet systems, as long as their subsystems are quantum chaotic and not localized in some manner. To calculate the generalized moments of the Schmidt eigenvalues in the perturbative regime, a regularized theory is applied, whose leading-order behaviors depend on root Lambda. The marginal case of the 1/2 moment, which is related to the distance to the closest maximally entangled state, is an exception having a root Lambda ln Lambda leading order and a logarithmic dependence on subsystem size. A recursive embedding of the regularized perturbation theory gives a simple exponential behavior for the von Neumann entropy and the Havrda-Charvat-Tsallis entropies for increasing interaction strength, demonstrating a universal transition to nearly maximal entanglement. Moreover, the full probability densities of the Schmidt eigenvalues, i.e., the entanglement spectrum, show a transition from power laws and Levy distribution in the weakly interacting regime to random matrix results for the strongly interacting regime. The predicted behaviors are tested on a pair of weakly interacting kicked rotors, which follow the universal behaviors extremely well.

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Language(s): eng - English
 Dates: 2018-09-142018-09
 Publication Status: Issued
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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: - Volume / Issue: 98 (3) Sequence Number: 032209 Start / End Page: - Identifier: ISSN: 1539-3755
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012