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arXiv:1009.4384 · Journal of Physics B Atomic Molecular and Optical Physics

Tripartite thermal correlations in an inhomogeneous spin–star system

Fabio Anzà, B Militello, A Messina

Published Oct 4, 2010• 27 citations
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Abstract

We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is, the three outer spins interacting with the central one in a spin–star system. We analyse the dependence of such correlations on the homogeneity of interactions, starting from the case where central–outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.

DOI
10.1088/0953-4075/43/20/205501

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We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is, the three outer spins interacting with the central one in a spin–star system. We analyse the dependence of such correlations on the homogeneity of interactions, starting from the case where central–outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.
We investigate the quantum discord in the thermal states for a spin-star model consisting of three parties which include one central spin and the other two outer spins. Our results imply that the quantum correlation can be established between the two outer spins both of which interacting with the central spin independently. From the analysis, we find that the quantum discord and entanglement depends not only on the external magnetic field and the interaction strength but also on the anisotropy parameter and the temperature. Specially, the quantum discord is more robust than the quantum entanglement in the sense that the quantum discord lasts for higher temperatures than the entanglement does.
In this paper, we study the thermal evolution of three types of quantum correlations under the homogeneous and inhomogeneous spin star Hamiltonian. It is shown that quantum discord (QD) is more stable than the other measures in the thermal regime, but concurrence is more efficient when the Hamiltonian parameters are employed. However, all quantum correlations can reach their maximum, if the inhomogeneous parameter raises. Quantum correlations can be enhanced by a weak external magnetic field and strong coupling parameter. But they vanish in the case of a strong magnetic field, weak coupling parameter, and high temperatures.
The spatial distribution of entanglement within a spin-1/2 Heisenberg star composed from a single central spin and three peripheral spins is examined in the presence of an external magnetic field using the Kambe projection method, which allows an exact calculation of the bipartite and tripartite negativity serving as a measure of the bipartite and tripartite entanglement. Apart from a fully separable polarized ground state emergent at high-enough magnetic fields, the spin-1/2 Heisenberg star exhibits at lower magnetic fields three outstanding nonseparable ground states. The first quantum ground state exhibits the bipartite and tripartite entanglement over all possible decompositions of the spin star into any pair or triad of spins, whereby the bipartite and tripartite entanglement between the central and peripheral spins dominates over that between the peripheral spins. The second quantum ground state has a remarkably strong tripartite entanglement between any triad of spins in spite of the lack of bipartite entanglement. The central spin of the spin star is separable from the remaining three peripheral spins within the third quantum ground state, where the peripheral spins are subject to the strongest tripartite entanglement arising from a two-fold degenerate W-state.
Heat capacity of a mixed-three-spin (1/2,1,1/2) antiferromagnetic XXX Heisenberg chain is precisely investigated by use of the partition function of the system for which, spins (1,1/2) have coupling constant [Formula: see text] and spins (1/2,1/2) have coupling constant [Formula: see text]. We verify tripartite entanglement for the model by means of the convex roof extended negativity (CREN) and concurrence as functions of temperature T, homogeneous magnetic field B and the coupling constants [Formula: see text] and [Formula: see text]. As shown in our previous work, [H. A. Zad, Chin. Phys. B 25 (2016) 030303.] the temperature, the magnetic field and the coupling constants dependences of the heat capacity for such spin system have different behaviors for the entangled and separable states, hence, we did some useful comparisons between this quantity and negativities of its organized bipartite (sub)systems at entangled and separable states. Here, we compare the heat capacity of the mixed-three-spin (1/2,1,1/2) system with the CREN and the tripartite concurrence (as measures of the tripartite entanglement) at low temperature. Ground state phase transitions, and also, transition from ground state to some excited states are explained in detail for this system at zero temperature. Finally, we investigate the heat capacity behavior around those critical points in which these quantum phase transitions occur.