Conservation laws protect dynamic spin correlations from decay: Limited role of integrability in the central spin model
Abstract
Mazur's inequality renders statements about persistent correlations possible. We generalize it in a convenient form applicable to any set of linearly independent constants of motion. This approach is used to show rigorously that a fraction of the initial spin correlations persists indefinitely in the isotropic central spin model unless the average coupling vanishes. The central spin model describes a major mechanism of decoherence in a large class of potential realizations of quantum bits. Thus the derived results contribute significantly to the understanding of the preservation of coherence. We will show that persisting quantum correlations are not linked to the integrability of the model but are caused by a finite operator overlap with a finite set of constants of motion.
 Publication:

Physical Review B
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevB.90.060301
 arXiv:
 arXiv:1402.1277
 Bibcode:
 2014PhRvB..90f0301U
 Keywords:

 78.67.Hc;
 02.30.Ik;
 03.65.Yz;
 72.25.Rb;
 Quantum dots;
 Integrable systems;
 Decoherence;
 open systems;
 quantum statistical methods;
 Spin relaxation and scattering;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 5 pages, 1 figure, +2 pages supplemental material Small changes and some additional explicit calculations in the supplement