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arXiv:1510.05838 · Physical review. B./Physical review. B

Using Majorana spin- 12 representation for the spin-boson model

Pablo Schad, Alexander Shnirman, Yuriy Makhlin

Published May 20, 2016• 12 citations
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Abstract

In this paper we resolve a contradiction between the fact that the method based on the Majorana representation of spin-$\frac{1}{2}$ is exact and its failure to reproduce the perturbative Bloch-Redfield relaxation rates. Namely, for the spin-boson model, direct application of this method in the leading order allows for a straightforward computation of the transverse spin correlations; however, for the longitudinal spin correlations it apparently fails in the long-time limit. Here we indicate the reason for this failure. Moreover, we suggest how to apply this method to allow, nevertheless, for simple and accurate computations of spin correlations. Specifically, we demonstrate that accurate results are obtained by avoiding the use of the longitudinal Majorana fermion and that correlations of the remaining transverse Majorana fermions can be easily evaluated using an effective Gaussian action.

DOI
10.1103/physrevb.93.174420

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