Energy current and its statistics in the nonequilibrium spin-boson model: Majorana fermion representation

TL;DR

This paper develops an analytical framework using Majorana fermions and Keldysh Green's functions to analyze energy transfer statistics in the nonequilibrium spin-boson model, revealing detailed heat current behavior and fluctuation symmetry.

Contribution

It introduces a novel analytical method combining Majorana fermion representation with Green's functions for the spin-boson model, deriving exact expressions for energy transfer statistics.

Findings

Derived the cumulant generating function satisfying fluctuation symmetry.

Obtained analytical heat current and noise expressions beyond simple regimes.

Validated results against quantum bounds and compared with other models.

Abstract

We study the statistics of thermal energy transfer in the nonequilibrium (two-bath) spin-boson model. This quantum many-body impurity system serves as a canonical model for quantum energy transport. Our method makes use of the Majorana fermion representation for the spin operators, in combination with the Keldysh nonequilibrium Green's function approach. We derive an analytical expression for the cumulant generating function of the model in the steady state limit, and show that it satisfies the Gallavotti-Cohen fluctuation symmetry. We obtain analytical expressions for the heat current and its noise, valid beyond the sequential and the co-tunnelling regimes. Our results satisfy the quantum mechanical bound for heat current in interacting nanojunctions. Results are compared with other approximate theories, as well as with a non-interacting model, a fully harmonic thermal junction.