Spin dynamics from Majorana fermions

TL;DR

This paper presents a method using Majorana fermions to directly compute spin dynamics and susceptibility, applied to a quantum dot system, revealing voltage-dependent relaxation and susceptibility behaviors.

Contribution

It introduces a novel approach to extract spin correlation functions from Majorana fermion propagators, applicable to non-equilibrium quantum systems.

Findings

Voltage-dependent spin relaxation rate in quantum dots

Confirmation of voltage-dependent Curie susceptibility

Method enables direct reading of spin dynamics from Majorana fermions

Abstract

Using the Majorana fermion representation of spin-1/2 local moments, we show how it is possible to directly read off the dynamic spin correlation and susceptibility from the one-particle propagator of the Majorana fermion. We illustrate our method by applying it to the spin dynamics of a non-equilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltage-dependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B {\bf 66}, 085315 (2002)].