Using Majorana spin-1/2 representation for the spin-boson model

TL;DR

This paper explores the use of Majorana spin-1/2 representation to analyze the spin-boson model, providing a simplified and effective approach for calculating spin correlations, especially transverse ones.

Contribution

It demonstrates how to accurately compute spin correlations in the spin-boson model using Majorana fermions, avoiding issues with longitudinal correlations.

Findings

Accurate transverse-spin correlation calculations using Majorana representation.

Identification of limitations in applying the method to longitudinal correlations.

Effective Gaussian action simplifies correlation evaluations.

Abstract

The Majorana representation for spin operators enables efficient application of field-theoretical methods for the analysis of spin dynamics. Moreover, a wide class of spin correlation functions can be reduced to Majorana correlations of the same order, simplifying their calculation. For the spin-boson model, direct application of this method in the lowest 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 and discuss, how this method can be used as a convenient and accurate tool for generic 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.