Spectrum and screening cloud in the central spin model

Michael Bortz, Sebastian Eggert, and Joachim Stolze
Phys. Rev. B 81, 035315 – Published 11 January 2010

Abstract

We consider an electronic spin in a quantum dot, coupled to the surrounding nuclear spins via inhomogeneous antiferromagnetic hyperfine interactions and subject to a uniform field, which is described by Gaudin’s central spin model. We study spectral properties, the two-point correlation functions, and the magnetization profile in the ground state and in low-lying excited states, which characterizes the structure of the cloud of nuclear spins screening the electron spin. A close connection to the pair-occupation probability in the BCS model is established. Using the exact Bethe-Ansatz solution of that model and arguments of integrability, we can distinguish between contributions from purely classical physics and from quantum fluctuations.

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  • Received 10 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.035315

©2010 American Physical Society

Authors & Affiliations

Michael Bortz1,*, Sebastian Eggert1, and Joachim Stolze2

  • 1Fachbereich Physik und Research Center OPTIMAS, Technische Universität Kaiserslautern, Erwin-Schrödinger-Strasse, D-67663 Kaiserslautern, Germany
  • 2Institut für Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany

  • *bortz@physik.uni-kl.de

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Vol. 81, Iss. 3 — 15 January 2010

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