RG transport theory for open quantum systems: Charge fluctuations in multilevel quantum dots in and out of equilibrium

TL;DR

This paper introduces a real-time renormalization group method to accurately analyze charge fluctuations in multi-level quantum dots under nonequilibrium conditions, demonstrating its effectiveness across various coupling strengths and temperatures.

Contribution

The paper develops a simplified RTRG approach that reliably describes charge fluctuations in quantum dots, validated against NRG and FRG data, especially at weak to intermediate coupling.

Findings

RTRG accurately describes charge fluctuations in quantum dots.

Good agreement with NRG and FRG data in relevant regimes.

Method is efficient for theoretical analysis of quantum dot charge dynamics.

Abstract

We present the real-time renormalization group (RTRG) method as a method to describe the stationary state current through generic multi-level quantum dots with a complex setup in nonequilibrium. The employed approach consists of a very rudiment approximation for the RG equations which neglects all vertex corrections while it provides a means to compute the effective dot Liouvillian self-consistently. Being based on a weak-coupling expansion in the tunneling between dot and reservoirs, the RTRG approach turns out to reliably describe charge fluctuations in and out of equilibrium for arbitrary coupling strength, even at zero temperature. We confirm this in the linear response regime with a benchmark against highly-accurate numerically renormalization group data in the exemplary case of three-level quantum dots. For small to intermediate bias voltages and weak Coulomb interactions, we find an excellent agreement between RTRG and functional renormalization group data, which can be expected to be accurate in this regime. As a consequence, we advertise the presented RTRG approach as an efficient and versatile tool to describe charge fluctuations theoretically in quantum dot systems.