Abstract
We consider a generalized spin star configuration that can be solved exactly, with the central spin-1/2 system embedded in an outer ring of N spin-1/2 particles (denoted as spin bath). In this model, we consider a modified version of the spin star model, by taking into account, besides the interaction of the central spin with the bath, the interactions between the spins of the bath as well. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of the symmetries of system. We then investigate the properties of the ground quantum phase transitions in some limiting cases in the model and show that the occurrence of quantum phase transitions and the desired ground states can be obtained by varying the external control parameters.
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