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Entanglement entropy scaling laws and eigenstate typicality in free fermion systems

Hsin-Hua Lai and Kun Yang
Phys. Rev. B 91, 081110(R) – Published 23 February 2015

Abstract

We demonstrate that the entanglement entropy area law for free fermion ground states and the corresponding volume law for highly excited states are related by a position-momentum duality, and thus are of the same origin. For a typical excited state in the thermodynamic limit, we further show that the reduced density matrix of a subsystem approaches the thermal density matrix, provided the subsystem's linear size is small compared to that of the whole system in all directions, a property we dub eigenstate typicality. This provides an explicit example of thermalization via entanglement, and reveals how statistical physics emerges from a single eigenstate by tracing out a large number of degrees of freedom.

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  • Received 17 September 2014
  • Revised 23 October 2014

DOI:https://doi.org/10.1103/PhysRevB.91.081110

©2015 American Physical Society

Authors & Affiliations

Hsin-Hua Lai1 and Kun Yang2

  • 1National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
  • 2Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA

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Issue

Vol. 91, Iss. 8 — 15 February 2015

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