Floquet Real-Time Renormalization Group

In this project, a renormalization group method for the description of open quantum systems is combined with Floquet theory. The method is applied to the Kondo model.

Resources

V. B., M. Pletyukhov, H. Schoeller and D. M. Kennes, Phys. Rev. B 106, 115440 (2022) (Download PDF)
Chapters 3 – 6 of my PhD thesis
Poster presented at the DPG condensed matter autumn meeting 2021 (Download PDF)

Collaborators

Dante M. Kennes, RWTH Aachen University and MPI for Structure and Dynamics of Matter
Mikhail Pletyukhov, RWTH Aachen University
Herbert Schoeller, RWTH Aachen University

Topic and Method

Kondo physics
Floquet theory in Liouville space (as used in Floquet Green's function formalism)
Real-time renormalization group [PRB 90.085121 / arXiv:1405.3150]

Developed Software

As part of this project I wrote a python library for working with Floquet matrices, which are theoretically infinitely large and require a careful treatment of truncation effects when used in numerical computation. This library uses the numpy C API, BLAS and LAPACK for best performance.

Also a python module for simpler handling of complicated RTRG-Floquet objects has been developed to make the implementation of RG equations more readable.

Interactive plots

The following plots are interactive versions of the figures in Phys. Rev. B 106, 115440. The explanation of the figures can be found in the paper. Here you find only short excerpts of the figure captions.

The python library>source code for obtaining these results is available online. The plots are generated using Plotly and D3.js.

Figure 2a: overview of differential conductance G average — Fig. 2a: Differential conductance G_avg=dI_avg/dV_avg for V(t)=V_avg+V_osccos(Ωt) as function of V_avg and V_osc at Ω=7.55T_K.

Figure 2b: overview of differential conductance G oscillating — Fig. 2b: Differential conductance G_osc=dI_osc/dV_osc for V(t)=V_avg+V_osccos(Ωt) as function of V_avg and V_osc at Ω=7.55T_K.

Figure 3: differential conductance G compared to approximations — Fig. 3: Differential conductance G_avg(V_avg,V_osc,Ω) from FRTRG (red line) compared to the adiabatic approximation (black dotted line), the phenomenological Eq. (160) (blue line), and the analytic approximation for limiting cases from [PhysRevB 62.8154 (2000)] (dashed lines in (c)–(d)). We use Ω = 7.55TK as in Fig. 2 except in panel (c).

Figure 4: comparison to an experiment — Fig. 4: Comparison to experiment by Kogan et al. (2004): Science 304 (5675) 1293-1295. Copyright of the experimental data: A. Kogan et al.

Figure 6: response to a short Gaussian voltage pulse — Fig. 6: Current and differential conductance G(t) as function of time after a short Gaussian voltage pulse of different height.

Comparison to an experiment by Bruhat, et al. [PRB 98.075121 (2018)] — Comparison of calculations (solid lines) to an experiment by Bruhat et al., Phys. Rev. B 98, 075121 (2018) (colored points). Different colors show different values for the oscillating voltage V_osc. The left panel shows a driving frequency of 19GHz and the right panel shows 12GHz. The solid lines include an adiabatic background conductance taken from the measurement at V_osc=20μV.