Spin- and entanglement-dynamics in the central-spin model with homogeneous couplings
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Date
2007
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IOP Publishing
Abstract
We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviours are found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question of to what extent entanglement of the bath spins prevents decoherence of the central spin.
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Keywords
entanglement in extended quantum systems (theory), quantum dots (theory), rigorous results in statistical mechanics
Citation
Bortz, Michael; Stolze, Joachim: Spin- and entanglement-dynamics in the central-spin model with homogeneous couplings. In: Journal of Statistical Mechanics 2007, P06018, doi: 10.1088/1742-5468/2007/06/P06018.