Current noise of the interacting resonant level model

Abstract

We study the zero-frequency current noise of the interacting resonant level model for arbitrary bias voltages using a functional renormalization group approach. For this we extend the existing nonequilibrium scheme by deriving and solving flow equations for the current-vertex functions. On-resonance artificial divergences of the latter found in lowest-order perturbation theory in the two-particle interaction are consistently removed. Away from resonance they are shifted to higher orders. This allows us to gain a comprehensive picture of the current noise in the scaling limit. At high bias voltages, the current noise exhibits a universal power-law decay, whose exponent is, to leading order in the interaction, identical to that of the current. The effective charge on resonance is analyzed in detail, employing properties of the vertex correction. We find that it is only modified to second or higher order in the two-particle interaction.

Out-of-equilibrium transport in the interacting resonant level model: Surprising relevance of the boundary sine-Gordon model

“…This extends a result of Ref. [35], which stated that the effective charge is e 1 + O(U 2 ) , and which was therefore relevant only in the vicinity of the noninteracting RLM.…”

“…The later is also the exponent b(U ) describing the current decay in the large rescaled bias regime. The fact that the current and the shot noise decay with the same exponent in the UV regime has already been noticed in [35] for small (perturbative) U , but it is observed here to hold at large U too.…”

“…[7,19], using a modified time-evolution with an explicit counting field χ, the cumulant generating function F was estimated numerically and the noise was extracted as the coefficient of the χ 2 term. More recently, a functional renormalization group approach [34] was used to compute the noise in the IRLM [35] [52], especially in the regime of small U . Instead, here we compute the current noise numerically using the relation between S and the fluctuations of the charge, as described by Eq.…”