Dicke model: entanglement as a finite size effect
We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a Bose-Einstein condensate at a threshold coupling. We...
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| Abstract | We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a Bose-Einstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state, which can be tested by probing two parts of the spin system separately, but only in a narrow regime around the threshold coupling. Around the resonance, the size of this regime is inversely proportional to the number of spins and shrinks down to zero for infinite systems. This spin entanglement is a non-perturbative effect and is also missed by the mean-field approximation. |
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| AbstractList | J. Phys.: Conf. Ser. 193, 012134(2009) We analyze Dicke model at zero temperature by matrix diagonalization to
determine the entanglement in the ground state. In the infinite system limit
the mean field approximation predicts a quantum phase transition from a
non-interacting state to a Bose-Einstein condensate at a threshold coupling. We
show that in a finite system the spin part of the ground state is a bipartite
entangled state, which can be tested by probing two parts of the spin system
separately, but only in a narrow regime around the threshold coupling. Around
the resonance, the size of this regime is inversely proportional to the number
of spins and shrinks down to zero for infinite systems. This spin entanglement
is a non-perturbative effect and is also missed by the mean-field
approximation. We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a Bose-Einstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state, which can be tested by probing two parts of the spin system separately, but only in a narrow regime around the threshold coupling. Around the resonance, the size of this regime is inversely proportional to the number of spins and shrinks down to zero for infinite systems. This spin entanglement is a non-perturbative effect and is also missed by the mean-field approximation. |
| Author | Loss, D Tsyplyatyev, O |
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| BackLink | https://doi.org/10.1088/1742-6596/193/1/012134$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.0907.2553$$DView paper in arXiv |
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| DOI | 10.48550/arxiv.0907.2553 |
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| Snippet | We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean... J. Phys.: Conf. Ser. 193, 012134(2009) We analyze Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state.... |
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| SubjectTerms | Approximation Coupling Entanglement Ground state Mathematical analysis Phase transitions Physics - Mesoscale and Nanoscale Physics Quantum theory Size effects |
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| Title | Dicke model: entanglement as a finite size effect |
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