Quantum correlations in the collective spin systems

Abstract

Quantum and classical pairwise correlations in two typical collective spin systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are discussed. These correlations in the thermodynamical limit are obtained analytically and in a finite-size system are calculated numerically. Large-size scaling behavior for the quantum discord itself is observed, which has never been reported in another critical system. A logarithmic diverging behavior for the first derivative of the quantum discord is also found in both models, which might be universal in the second-order quantum phase transition. It is suggested that the pronounced maximum or minimum of first derivative of quantum discord signifies the critical point. Comparisons between the quantum discord and the scaled concurrence are performed. It is shown that the quantum discord is very small in one phase and robust in the other phase, while the scaled concurrence shows maximum at the critical point and decays rapidly when away from the the critical point.

8 pages, 4 figures

References in corpus (12)

• Quantum discord and the power of one qubit
• Experimental quantum computing without entanglement
• Quantum Phase Transitions and Bipartite Entanglement
• Quantum discord and quantum phase transition in spin chains
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Dicke quantum spin glass of atoms and photons
• Accurate numerical solution to the finite-size Dicke model
• Concurrence in collective models
• Finite-temperature mutual information in a simple phase transition
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Quantum discord and classical correlations in the bond-charge Hubbard model: quantum phase transitions, ODLRO and violation of the monogamy property for discord
• Witnessing nonclassical multipartite states

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• Enhancing the geometric quantum discord in the Heisenberg {\it XX} chain by Dzyaloshinsky-Moriya interaction
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• Shareability of Quantum Correlations in a Many-Body Spin System with Two- and Three-Body Interactions