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Renormalization group for open quantum systems using environment temperature as flow parameter

by K. Nestmann, M. R. Wegewijs

This Submission thread is now published as SciPost Phys. 12, 121 (2022)

Submission summary

As Contributors: Konstantin Nestmann · Maarten Wegewijs
Arxiv Link: (pdf)
Date accepted: 2022-03-23
Date submitted: 2022-03-17 11:54
Submitted by: Nestmann, Konstantin
Submitted to: SciPost Physics
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


We present the $T$-flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature $T$ of its environment. This has the key advantage that it can be formulated directly in real time, making it particularly suitable for transient dynamics, while automatically accumulating the full temperature dependence of transport quantities. We solve the $T$-flow equations numerically for the example of the single impurity Anderson model. We benchmark in the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger using results obtained by the functional renormalization group, density-matrix renormalization group and the quantum Monte Carlo method. Here we find quantitative agreement even in the worst case of strong interactions and low temperatures, indicating the reliability of the method. For transient charge currents we find good agreement with results obtained by the 2PI Green's function approach. Furthermore, we analytically show that the short-time dynamics of both local and non-local observables follow a universal temperature-independent behaviour when the metallic reservoirs have a flat wide band.

Published as SciPost Phys. 12, 121 (2022)

List of changes

* Added a new Appendix D, which discusses the flow equations for different temperatures
* Added the new Appendix F "Exact solution for $U=0$"
* Several clarifications in response to the referees (see replies)
* We noted that Fig. 2b contained curves which were insufficiently converged. This has been corrected without affecting any part of the text and conclusions.

Reports on this Submission

Anonymous Report 2 on 2022-3-21 (Invited Report)


same as in my first report




I tend to accept the authors' arguments regarding my comments from the first report. I also appreciate the changes made to the manuscript in response to my questions. The article can now be published as it is.

Requested changes


  • validity: top
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2022-3-19 (Invited Report)


all requested changes were taken into account in a satisfactory way.
I recommend to accept for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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