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

Steven Tomsovic, Arul Lakshminarayan, Shashi C. L. Srivastava, and Arnd Bäcker
Phys. Rev. E 98, 032209 – Published 14 September 2018

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 Λ. 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 Λ. 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 ΛlnΛ 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-Charvát-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 Lévy 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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  • Received 2 July 2018

DOI:https://doi.org/10.1103/PhysRevE.98.032209

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Steven Tomsovic1,2,3, Arul Lakshminarayan1,4, Shashi C. L. Srivastava1,5,6, and Arnd Bäcker1,2

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
  • 2Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
  • 3Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA
  • 4Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
  • 5Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India
  • 6Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400085, India

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Issue

Vol. 98, Iss. 3 — September 2018

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