Functional renormalization group in Floquet space

TL;DR

This paper extends the functional renormalization group method to Floquet space, enabling analysis of long-term behavior in interacting periodically driven quantum dots without restrictions on driving amplitude or frequency.

Contribution

It introduces a general Floquet space extension of the functional renormalization group applicable to various driving parameters and provides analytic and numerical insights into the renormalization process.

Findings

Driving frequency acts as an infrared cutoff in the renormalization flow.

Shape of the reservoir distribution function influences the renormalization.

Power-law behavior in the mean current reflects the driving frequency dependence.

Abstract

We present an extension of the functional renormalization group to Floquet space, which enables us to treat the long time behavior of interacting time periodically driven quantum dots. It is one of its strength that the method is neither bound to small driving amplitudes nor to small driving frequencies, i.e. very general time periodic signals can be considered. It is applied to the interacting resonant level model, a prototype model of a spinless, fermionic quantum dot. The renormalization in several setups with different combinations of time periodic parameters is studied, where the numerical results are complemented by analytic expressions for the renormalization in the limit of small driving amplitude. We show how the driving frequency acts as an infrared cutoff of the underlying renormalization group flow which manifests in novel power laws. We utilize the tunability of the effective reservoir distribution function in a periodically driven onsite energy setup to show how its shape is directly reflected in the renormalization group flow. This allows to flexibly tune the power-law renormalization generically encountered in quantum dot structures. Finally, an in-phase quantum pump as well as a single parameter pump are investigated in the whole regime of driving frequency, demonstrating that the new power law in the driving frequency is reflected in the mean current of the latter.