Fermionic entanglement in the Lipkin model

M. Di Tullio, R. Rossignoli, M. Cerezo, and N. Gigena
Phys. Rev. A 100, 062104 – Published 3 December 2019

Abstract

We examine the fermionic entanglement in the ground state of the fermionic Lipkin model and its relation with bipartite entanglement. It is first shown that the one-body entanglement entropy, which quantifies the minimum distance to a fermionic Gaussian state, behaves similarly to the mean-field order parameter and is essentially proportional to the total bipartite entanglement between the upper and lower modes, a quantity meaningful only in the fermionic realization of the model. We also analyze the entanglement of the reduced state of four single-particle modes (two up-down pairs), showing that its fermionic concurrence is strongly peaked at the phase transition and behaves differently from the corresponding up-down entanglement. We finally show that the first measures and the up-down reduced entanglement can be correctly described through a basic mean-field approach supplemented with symmetry restoration, whereas the concurrence requires at least the inclusion of random-phase-approximation–type correlations for a proper prediction. Fermionic separability is also discussed.

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  • Received 21 August 2019

DOI:https://doi.org/10.1103/PhysRevA.100.062104

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Di Tullio1, R. Rossignoli1,2, M. Cerezo3, and N. Gigena1

  • 1IFLP/CONICET and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata (1900), Argentina
  • 2Comisión de Investigaciones Científicas (CIC), La Plata (1900), Argentina
  • 3Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Issue

Vol. 100, Iss. 6 — December 2019

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