Oguri相互作用费米子线性电导公式的Keldysh推导
Keldysh Derivation of Oguri's Linear Conductance Formula for Interacting Fermions
摘要：
我们提出了一个基于凯尔迪什的公式推导，该公式是由Oguri使用松原公式获得的，用于通过与非相互作用费米子引线耦合的中心相互作用区域的线性电导。我们的出发点是著名的梅尔-温格伦电流公式，其导数w.r.t.与源极-漏极电压的关系产生电导。我们利用泛函重整化群的精确流动方程来解析地执行这个导数，该方程表示流动w.r.t.两粒子顶点的自能电压。这就产生了一个基于凯尔迪什的公式的小栗公式的线性电导，这有利于将其应用在凯尔迪什形式主义制定的近似方案的上下文中。（将我们的方法推广到非线性电导是简单的，但在这里不进行。--我们在一个模型的背景下说明了我们的线性电导公式，该模型先前已被证明可以在0.7异常区域捕获量子点接触的基本物理学。该模型涉及具有一维势垒和现场相互作用的紧束缚链，我们使用二阶微扰理论来处理。我们表明，数值计算的成本可以显着降低，通过使用非均匀的晶格间距，选择这样的人工束缚态靠近上带边的发生是避免的。
英文摘要：
We present a Keldysh-based derivation of a formula, previously obtained by Oguri using the Matsubara formalisum, for the linear conductance through a central, interacting region coupled to non-interacting fermionic leads. Our starting point is the well-known Meir-Wingreen formula for the current, whose derivative w.r.t.\ to the source-drain voltage yields the conductance. We perform this derivative analytically, by exploiting an exact flow equation from the functional renormalization group, which expresses the flow w.r.t.\ voltage of the self-energy in terms of the two-particle vertex. This yields a Keldysh-based formulation of Oguri's formula for the linear conductance, which facilitates applying it in the context of approximation schemes formulated in the Keldysh formalism. (Generalizing our approach to the non-linear conductance is straightforward, but not pursued here.) -- We illustrate our linear conductance formula within the context of a model that has previously been shown to capture the essential physics of a quantum point contact in the regime of the 0.7 anomaly. The model involves a tight-binding chain with a one-dimensional potential barrier and onsite interactions, which we treat using second order perturbation theory. We show that numerical costs can be reduced significantly by using a non-uniform lattice spacing, chosen such that the occurence of artificial bound states close to the upper band edge is avoided.
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