Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models

Lucas Hackl, Lev Vidmar, Marcos Rigol, and Eugenio Bianchi
Phys. Rev. B 99, 075123 – Published 11 February 2019

Abstract

We recently showed [Phys. Rev. Lett. 121, 220602 (2018)] that the average bipartite entanglement entropy of all energy eigenstates of the quantum Ising chain exhibits a universal (for translationally invariant quadratic fermionic models) leading term that scales linearly with the subsystem's volume, while in the thermodynamic limit the first subleading correction does not vanish at the critical field (it only depends on the ratio f between the volume of the subsystem and volume of the system) and vanishes otherwise. Here we show, analytically for bounds and numerically for averages, that the same remains true for the spin-1/2 XY chain in a transverse magnetic field. We then tighten the bounds for the coefficient of the universal volume-law term, which is a concave function of f. We develop a systematic approach to compute upper and lower bounds, and we provide explicit analytic expressions for up to the fourth-order bounds.

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  • Received 20 December 2018
  • Revised 25 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.075123

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Lucas Hackl1,2,3, Lev Vidmar4, Marcos Rigol3, and Eugenio Bianchi2,3

  • 1Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, D-85748 Garching bei München, Germany
  • 2Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 3Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 4Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia

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Issue

Vol. 99, Iss. 7 — 15 February 2019

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