TY - JOUR

T1 - Spin and entanglement dynamics in the central-spin model with homogeneous couplings

AU - Bortz, Michael

AU - Stolze, Joachim

PY - 2007/6/1

Y1 - 2007/6/1

N2 - 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.

AB - 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.

KW - Entanglement in extended quantum systems (theory)

KW - Quantum dots (theory)

KW - Rigorous results in statistical mechanics

UR - http://www.scopus.com/inward/record.url?scp=34548666794&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2007/06/P06018

DO - 10.1088/1742-5468/2007/06/P06018

M3 - Article

SN - 1742-5468

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 6

M1 - P06018

ER -