Title: Fermionic entanglement in the Lipkin model

Journal Article · · Physical Review A
ORCiD logo [1]; ORCiD logo [2];  [3];  [1]
  1. Univ. Nacional de La Plata (Argentina)
  2. Univ. Nacional de La Plata (Argentina); Comisión de Investigaciones Científicas (CIC), La Plata (Argentina)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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Here, 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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1739972
Report Number(s):
LA-UR--19-27998
Journal Information:
Physical Review A, Journal Name: Physical Review A Journal Issue: 6 Vol. 100; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Fermionic
Lipkin
approximation methods for many-body systems
entanglement
exact solutions for many-body systems
fermionic condensates
information science
magnetic systems
mean field theory
model
quantum correlations in quantum information
quantum entanglement
quantum phase transitions