We study relaxation dynamics in a strongly interacting two-site Fermi-Hubbard model that is induced by coupling each site to a local fermionic bath. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the time evolution of the reduced density matrix. In spite of a local coupling to the baths, the found Lindblad operators are nonlocal in space. We compare with the local approximation, where those nonlocal effects are neglected. Furthermore, we propose an improvement on the commonly used secular approximation (rotating-wave approximation), referred to as coherent approximation, which turns out superior in all studied parameter regimes (and equivalent otherwise). We look at the relaxation dynamics for several important observables and compare the methods for early and late times in various temperature regimes.

中文翻译：

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哈伯二聚体与铁离子浴耦合的弛豫动力学：现象学描述及其微观基础

我们研究了强相互作用的两个位点的费米-哈伯德模型中的松弛动力学，该模型是通过将每个位点耦合到局部铁离子浴而诱导的。为了得出输入Lindblad算子的正确形式，以对不同温度范围内的系统-浴耦合进行有效描述，我们采用了图解实时技术来简化密度矩阵的时间演化。尽管与浴池局部耦合，但发现的Lindblad算子在空间中不是局部的。我们与局部近似比较，忽略了这些非局部影响。此外，我们提出了对常用的世俗逼近（旋转波逼近）的一种改进，称为相干逼近，在所有研究的参数体系（以及其他等效参数）中均表现出优越性。