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

TL;DR

This paper introduces a novel theoretical approach using Majorana-Fermion representation and polaron transformation to analyze Green's functions in the spin-boson model, providing reliable results across various regimes and extending beyond conventional perturbation theories.

Contribution

The authors develop a new method combining Majorana-Fermion representation and polaron transformation to analyze Green's functions in the spin-boson model, surpassing traditional perturbation approaches.

Findings

The approach yields consistent susceptibility and SSCF results in Ohmic and sub-Ohmic baths.

The SSCF matches NIBA in unbiased systems and extends applicability to biased, wider temperature ranges.

The method confirms the quantum-to-classical mapping validity in the entire sub-Ohmic regime.

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.