Scaling Theory of Entanglement at the Many-Body Localization Transition

Philipp T. Dumitrescu, Romain Vasseur, and Andrew C. Potter
Phys. Rev. Lett. 119, 110604 – Published 14 September 2017
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Abstract

We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a subthermal volume law, whose coefficient is a universal scaling function. The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume law on the thermal side, to pure area law on the MBL side.

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  • Received 23 January 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.110604

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyAtomic, Molecular & OpticalStatistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Philipp T. Dumitrescu1,*, Romain Vasseur2,3,4, and Andrew C. Potter1

  • 1Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
  • 2Department of Physics, University of California, Berkeley, California 94720, USA
  • 3Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA
  • 4Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA

  • *philippd@utexas.edu

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Issue

Vol. 119, Iss. 11 — 15 September 2017

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