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, Eugenio Bianchi

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2 Citations (Scopus)

Abstract

We recently showed [Phys. Rev. Lett. 121, 220602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.220602] 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.

Original languageEnglish (US)
Article number075123
JournalPhysical Review B
Volume99
Issue number7
DOIs
StatePublished - Feb 11 2019

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eigenvectors
Entropy
Thermodynamics
entropy
Magnetic fields
thermodynamics
coefficients
magnetic fields
energy

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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abstract = "We recently showed [Phys. Rev. Lett. 121, 220602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.220602] 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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AU - Hackl, Lucas

AU - Vidmar, Lev

AU - Rigol, Marcos

AU - Bianchi, Eugenio

PY - 2019/2/11

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N2 - We recently showed [Phys. Rev. Lett. 121, 220602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.220602] 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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