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arXiv:nlin/0208031

Comment on: ``Semiclassical theory of spin-orbit interactions using spin coherent states''

Jens Bolte, Rainer Glaser, Stefan Keppeler

Published Aug 23, 2002• 0 citations
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Abstract

We point out that a certain kind of combined classical translational and spin dynamics -- claimed in [M. Pletyukhov, et al. Phys. Rev. Lett. 89 (2002) 116601] to arise from the Pauli equation in the semiclassical limit $\hbar\to0$ for fixed spin -- only shows up if one simultaneously considers the high spin limit $S\to\infty$.

DOI
10.48550/arxiv.nlin/0208031

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We point out that a certain kind of combined classical translational and spin dynamics -- claimed in [M. Pletyukhov, et al. Phys. Rev. Lett. 89 (2002) 116601] to arise from the Pauli equation in the semiclassical limit ℏ→0\hbar\to0ℏ→0 for fixed spin -- only shows up if one simultaneously considers the high spin limit S→∞S\to\inftyS→∞.
We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin–orbit interactions and the Jaynes–Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin-1/2.
Comment on "High-Spin Polaron in Lightly Doped CuO2_22​ Planes"
In a recent Letter (Phys. Rev. Lett. 106, 036401 (2011)), Lau, et al. investigated the single hole problem in an effective model containing Cu ddd and O 2p2p2p orbitals by exact diagonalization on clusters composed of 32 CuO2_22​ unit cells. With full quantum fluctuations due to the antiferromagnetic (AFM) backgroud, they found that spin-polaron solutions with spin 3/2 become lowest energy solutions in certain region of Brillouin zone (BZ), which they claimed no similiar solutions were obtained in other models or approximations before. In this Comment, we would like to point out that such high-spin polaron solutions have been found in our previous Letter (Phys. Rev. Lett. 91, 057001, (2003)) and many of features described by Lau et al. have in fact been seen in our Letter.