Green’s functions for spin boson systems: Beyond conventional perturbation theories

Abstract

Unraveling general properties of Green's functions of quantum dissipative systems is of both experimental relevance and theoretical interest. Here, we study the spin-boson model as a prototype. By utilizing the Majorana-Fermion representation together with the polaron transformation, we establish a theoretical approach to analyze Green's functions of the spin-boson model. In contrast to conventional perturbation theories either in the tunneling energy or in the system-bath coupling strength, the proposed scheme gives reliable results over wide regimes of the coupling strength, bias, as well as temperature. To demonstrate the utility of the approach, we consider the susceptibility as well as the symmetrized spin correlation function (SSCF) which can be expressed in terms of Green's functions. Thorough investigations are made on systems embedded in Ohmic or sub-Ohmic bosonic baths. We found the so-obtained SSCF is the same as that of the non-interacting blip approximation (NIBA) in unbiased systems while it is applicable for a wider range of temperature in the biased systems compared with the NIBA. We also show that a previous perturbation result is recovered as a weak coupling limit of the so-obtained SSCF. Furthermore, by studying the quantum criticality of the susceptibility, we confirm the validity of the quantum-toclassical mapping in the whole sub-Ohmic regime.

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

“…We have further demonstrated that a heat diode becomes more effective as we increase the system-bath coupling. Additional improvements to the Majorana formulation presented here could be made, e.g., by developing a polarontransformed Majorana fermion-NEGF approach [57]. Future work will be focused on simulating counting statistics in the NESB model beyond perturbative approaches [35,58,59].…”

Heat transport in a two-level system driven by a time-dependent temperature

“…In particular, we extend the approach of Refs. [34,35] to include a time-dependent temperature. We start by performing a polaron transformation, which allows us to rewrite the coupling to the reservoirs in a manner that can be treated using perturbation theory [43][44][45].…”

“…2(b) for different coupling strengths. The imaginary part of the susceptibility quantifies the response of the qubit to external forces at a given frequency [34], and with a small susceptibility the qubit interacts only weakly with the environments, resulting in a small energy transfer. We note that the susceptibility can be related to a scattering matrix [29] and to the structure factor through fluctuation-dissipation theorems [53], which in turn quantifies the scattering of photons due to the interaction with the qubit [54].…”

“…To evaluate the time-dependent heat current, we extend the method of Refs. [34,35] for static systems to setups with time-dependent temperatures. We then apply this methodology to characterize the qubit as a thermal half-wave rectifier.…”

Heat transport in a two-level system driven by a time-dependent temperature

“…2b for different coupling strengths. The imaginary part of the susceptibility quantifies the response of the qubit to external forces at a given frequency [30], and with a small susceptibility the qubit interacts only weakly with the environments, resulting in a small energy transfer. We note that the susceptibility can be related to a scattering matrix [29], and to the structure factor through fluctuation-dissipation theorems [45], which in turn quantifies the scattering of photons due to the interaction with the qubit [46].…”