dorsal/arxiv
View SchemaBi-partite and global entanglement in a many-particle system with collective spin coupling
| Authors | R. G. Unanyan, C. Ionescu, M. Fleischhauer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412164 |
| URL | https://arxiv.org/abs/quant-ph/0412164 |
Abstract
Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions which includes the special case of a super-symmetry, the ground state can be constructed analytically. In the case of an anti-ferromagnetic coupling and for an even number of particles this state undergoes a smooth crossover as a function of the continuous anisotropy parameter $\gamma $ from a separable ($\gamma =\infty $) to a maximally entangled many-particle state ($\gamma =0$). From the analytic expression for the ground state, bipartite and global entanglement are calculated. In the thermodynamic limit a discontinuous change of the scaling behavior of the bipartite entanglement is found at the isotropy point $\gamma =0$. For $% \gamma =0$ the entanglement grows logarithmically with the system size with no upper bound, for $\gamma \neq 0$ it saturates at a level only depending on $\gamma $. For finite systems with total spin $J=N/2$ the scaling behavior changes at $\gamma =\gamma _{\mathrm{crit}}=1/J$.
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"date_created": "2026-03-02T18:02:12.709000Z",
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"abstract": "Bipartite and global entanglement are analyzed for the ground state of a\nsystem of $N$ spin 1/2 particles interacting via a collective spin-spin\ncoupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain\nconditions which includes the special case of a super-symmetry, the ground\nstate can be constructed analytically. In the case of an anti-ferromagnetic\ncoupling and for an even number of particles this state undergoes a smooth\ncrossover as a function of the continuous anisotropy parameter $\\gamma $ from a\nseparable ($\\gamma =\\infty $) to a maximally entangled many-particle state\n($\\gamma =0$). From the analytic expression for the ground state, bipartite and\nglobal entanglement are calculated. In the thermodynamic limit a discontinuous\nchange of the scaling behavior of the bipartite entanglement is found at the\nisotropy point $\\gamma =0$. For $% \\gamma =0$ the entanglement grows\nlogarithmically with the system size with no upper bound, for $\\gamma \\neq 0$\nit saturates at a level only depending on $\\gamma $. For finite systems with\ntotal spin $J=N/2$ the scaling behavior changes at $\\gamma =\\gamma\n_{\\mathrm{crit}}=1/J$.",
"arxiv_id": "quant-ph/0412164",
"authors": [
"R. G. Unanyan",
"C. Ionescu",
"M. Fleischhauer"
],
"categories": [
"quant-ph"
],
"title": "Bi-partite and global entanglement in a many-particle system with collective spin coupling",
"url": "https://arxiv.org/abs/quant-ph/0412164"
},
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