Tunneling-induced renormalization in interacting quantum dots

TL;DR

This paper investigates how tunneling processes cause quantum fluctuations and parameter renormalization in strongly interacting quantum dots, revealing opposite sign renormalizations for different charge states and verifying results with perturbation theory.

Contribution

It introduces a canonical transformation approach to analyze tunneling-induced fluctuations in strongly interacting quantum dots, highlighting the opposite renormalizations of tunnel couplings.

Findings

Tunnel couplings for different charge transitions renormalize with opposite signs.

Renormalization significantly affects conductance shape.

Results are consistent with second-order perturbation theory.

Abstract

We analyze tunneling-induced quantum fluctuations in a single-level quantum dot with arbitrarily strong onsite Coulomb interaction, generating cotunneling processes and renormalizing system parameters. For a perturbative analysis of these quantum fluctuations, we remove off-shell parts of the Hamiltonian via a canonical transformation. We find that the tunnel couplings for the transitions connecting empty and single occupation and connecting single and double occupation of the dot renormalize with the same magnitude but with opposite signs. This has an important impact on the shape of the renormalization extracted for example from the conductance. Finally, we verify the compatibility of our results with a systematic second-order perturbation expansion of the linear conductance performed within a diagrammatic real-time approach.