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Quantum phase transitions and quantum communication in a spin star system

We consider a generalized spin star system which can be solved exactly, with the central spin- system embedded in a bath of N spin- particles. In this system, in addition to the central–outer couplings, each pair of nearest neighbours of the bath spins interacts within themselves. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of symmetries of the system. We then investigate the quantum phase transitions in some limiting cases and show that the occurrence of the quantum phase transitions can be obtained by varying the external control parameters. We further analyse the properties of quantum communication in this model. In the time evolution, some simple and interesting results are discovered concerning transfer fidelity, cloning fidelity, as well as entanglements created.