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

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.