Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians - INSPIRE

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Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians

Lev Vidmar
(
- Penn State U.
)
,
Lucas Hackl
(
- Penn State U. and
- Penn State U., University Park, IGC
)
,
Eugenio Bianchi
(
- Penn State U. and
- Penn State U., University Park, IGC
)
,
Marcos Rigol
(
- Penn State U.
)

Mar 8, 2017

6 pages

Published in:

Phys.Rev.Lett. 119 (2017) 2, 020601

Published: Jul 11, 2017

e-Print:

1703.02979 [cond-mat.stat-mech]

DOI:

10.1103/PhysRevLett.119.020601

View in:

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Abstract: (APS)

In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is Save≃lnDA-(1/2)DA2/D for 1≪DA≤D, where DA and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnDA-(lnDA)2/lnD≤⟨S⟩≤lnDA-[1/(2ln2)](lnDA)2/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩

Note:

4+6 pages, 3+2 figures, as published

entropy: entanglement
dimension: 1
fermion: many-body problem
Hilbert space: dimension
Hamiltonian

References(35)

Figures(5)

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