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

### Submission summary

 As Contributors: Konstantin Nestmann · Maarten Wegewijs Arxiv Link: https://arxiv.org/abs/2111.07320v2 (pdf) Date accepted: 2022-03-23 Date submitted: 2022-03-17 11:54 Submitted by: Nestmann, Konstantin Submitted to: SciPost Physics Academic field: Physics Specialties: Quantum Physics Approach: Theoretical

### Abstract

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.

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 121 (2022)

Resubmission 2111.07320v2 on 17 March 2022
Submission 2111.07320v1 on 16 November 2021

## Reports on this Submission

### Strengths

same as in my first report

-

### 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

none

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

### Report

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

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