自旋玻色子系统的格林函数：超越常规微扰理论
Green's functions for spin boson systems: Beyond conventional perturbation theories
摘要：
揭示量子耗散系统格林函数的一般性质具有实验意义和理论意义。在这里，我们研究自旋玻色子模型作为一个原型。利用Majorana-Fermion表象和极化子变换，我们建立了一种分析自旋玻色子模型格林函数的理论方法。与传统的微扰理论相比，无论是在隧穿能量或在系统浴耦合强度，所提出的方案给出了可靠的结果，在广泛的制度的耦合强度，偏压，以及温度。为了证明该方法的实用性，我们考虑的磁化率以及对称化的自旋关联函数（SSCF），可以表示在格林函数。深入的调查是在系统嵌入欧姆或亚欧姆玻色子浴。我们发现，这样得到的SSCF是相同的无偏系统中的非相互作用blip近似（NIBA），而它是适用于更广泛的温度范围内的有偏系统相比，NIBA。我们还表明，以前的微扰结果恢复为弱耦合限制的如此获得的SSCF。此外，通过研究极化率的量子临界性，我们证实了量子到经典映射在整个亚欧姆区的有效性。
英文摘要：
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.
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