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Heyder, Jan; Bauer, Florian; Schimmel, Dennis; Delft, Jan von (2017): Derivation of Oguri's linear conductance formula for interacting fermions within the Keldysh formalism. In: Physical Review B, Vol. 96, No. 12, 125141
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Abstract

We present a Keldysh-based derivation of a formula, previously obtained by Oguri using the Matsubara formalism, for the linear conductance through a central, interacting region coupled to noninteracting fermionic leads. Our starting point is the well-known Meir-Wingreen formula for the current, whose derivative with respect 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 with respect to 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 nonlinear 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 nonuniform lattice spacing, chosen such that the occurrence of artificial bound states close to the upper band edge is avoided.