Nonequilibrium spin-boson model: from weak to strong coupling

Abstract

We present a general theory to explore energy transfer in nonequilibrium spin-boson models within the framework of nonequilibrium Green's function (NEGF). In contrast to conventionally used NEGF methods based on a perturbation expansion in the system-bath coupling, we adopt the polaron transformation to the Hamiltonian and identify the tunneling term as a perturbation with the system-bath coupling being treated nonperturbatively, herein termed the polaron-transformed NEGF method. To evaluate terms in the Dyson series, we further utilize the Majorana-fermion representation. The proposed method not only allows us to deal with weak as well as strong coupling regime, but also enables an investigation on the role of bias. As an application of the method, we study the energy transfer between two Ohmic bosonic baths mediated by a spin. For a unbiased spin system, our energy current result smoothly bridges predictions of two benchmarks, namely, the quantum master equation and the nonequilibrium non-interacting blip approximation, thus our method is beyond existing theories. In case of a biased spin system, we reveal a bias-induced nonmomotonic behavior of the energy conductance in the intermediate coupling regime, due to the resonant character of the energy transfer. This finding may offer a nontrivial quantum control knob over energy transfer at the nanoscale.