2014
DOI: 10.1103/physrevb.90.060301
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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 res… Show more

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Cited by 29 publications
(49 citation statements)
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“…We recall that the lower bounds as discussed in Refs. [25,26] result from the existence of conserved quantities such as the total angular momentum and the total energy. These quantities are conserved also for the classical model and the choices of couplings we are considering here.…”
Section: Long-time Behaviormentioning
confidence: 99%
See 1 more Smart Citation
“…We recall that the lower bounds as discussed in Refs. [25,26] result from the existence of conserved quantities such as the total angular momentum and the total energy. These quantities are conserved also for the classical model and the choices of couplings we are considering here.…”
Section: Long-time Behaviormentioning
confidence: 99%
“…Density-matrix renormalization group (DMRG) can tackle much larger systems up to about 1000 spins, but is restricted to short times up to about 40 /J Q [22][23][24]. The strict limit of infinite times, i.e., of persisting correlations has been tackled by mathematically rigorous bounds [25,26]. Techniques based on non-Markovian master equations give access to large bath sizes, but are well justified only for sufficiently strong external fields [27][28][29][30][31][32][33][34].…”
Section: Introductionmentioning
confidence: 99%
“…Adding the quadrupolar couplings H µ N has two effects on the nuclear spin dynamics: firstly it enhances the nuclear Larmor frequency, and, secondly, the breaking of the total spin conservation law translates into a change of an effective precession axis which is not longer determined by the carrier spin direction only. Both effects yields to an addition dephasing of the Overhauser field and consequently to a dephasing of the non-decaying fraction of the spin-correlation function [25] on a time scale dominated by the quadrupolar coupling strength.…”
Section: (E) and (F)mentioning
confidence: 99%
“…The separation of time scales [7] -a fast electronic precession around an effective nuclear magnetic field, and slow nuclear spin precessions around the fluctuating electronic spin -has motivated various semiclassical approximations [1,7,20,[23][24][25] which describe the short-time dynamics of the central spin polarization very well. As can be shown rigorously [26] the CSM predicts a finite non-decaying spin polarization [7,27,28] whose lower bound depends on the distribution function of the hyperfine couplings and is only linked to conservation laws. In semi-classical theories [7,27] it is given by a third of the initial spin polarization leading to a large spectral weight at zero-frequency in the spin-noise spectrum.…”
mentioning
confidence: 99%