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divERGe implements various Exact Renormalization Group examples

by Jonas B. Hauck, Dante M. Kennes, Lennart Klebl

This is not the latest submitted version.

Submission summary

Authors (as registered SciPost users): Lennart Klebl
Submission information
Preprint Link:  (pdf)
Code repository:
Date submitted: 2023-11-15 09:51
Submitted by: Klebl, Lennart
Submitted to: SciPost Physics Codebases
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU²FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

Current status:
Has been resubmitted

Submission & Refereeing History

Reports on this Submission

Report 2 by Claudio Attaccalite on 2023-12-18 (Contributed Report)

  • Cite as: Claudio Attaccalite, Report on arXiv:2311.07667v1, delivered 2023-12-18, doi: 10.21468/SciPost.Report.8275


-the paper is clear and guide the user step-by-step in the use of the code
-example are provided


-discussion on parallelization and scaling of the code can be enlarged


The manuscript presents a spet-by-spet use of the divERGe code for the exact renormalisation group. As it was a bit complicated to find additional reviewers, I decided to proceed with one report, plus some additional questions/remarks I would like to pose to the authors:

1) In the manuscript, parallelisation is barely mentioned in one or two places. Can the authors be more specific about what is being parallelized and how, and what part is GPU accelerated?

2) The authors mention the difficulty of available memory when parallelizing in MPI, have they considered parallelizing in openMP?

3) How does the code scale with system size, orbitals, k-points both in terms of computation time and memory usage?

4) Some of the ab-initio packages mentioned at the beginning of the manuscript also include code to estimate the V_{1,2,34} parameters, for example HP( in QuantumEspresso. Have the authors considered the possibility of linking their code to something similar?

  • validity: good
  • significance: good
  • originality: good
  • clarity: good
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2023-12-4 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2311.07667v1, delivered 2023-12-04, doi: 10.21468/SciPost.Report.8219


- the technical presentation and writing of the paper is excellent
- the software package seems very sophisticated and flexible
- documentation of the code appears fairly complete and exhaustive
- package interfaces with established ab-initio codes like Wannier90


- claim of "high-performance", but no benchmark or scaling plot is shown
- example scripts in the appendix are commented but not well-explained
- paper seems strongly expert-oriented in the current stage
- fRG is advocated as replacement of RPA for real materials, but on what basis?


The paper "divERGe implements various Exact Renormalization Group examples" by Hauck et al., describes the implementation of the divERGe software, a C++/python library for performing different types of momentum space functional renormalization group calculations, with an interface to standard ab-initio codes. Such an implementation is very welcome, as it allows fRG newcomers to set up their own calculations straightforwardly if an appropriate model Hamiltonian can be provided. The paper is clearly written and the "typology" of the code is detailed in-depth, with even more documentation available online. From my perspective, the manuscript definitely deserves publication, though three points need further clarification:

(1) The package is claimed to be "high-performance", but no scaling plots or benchmarks with similar implementations are shown. Furthermore, but this might be my mistake, I could not find an estimate of how much computational resources are needed to run a typical fRG calculation using divERGe. I think this might be useful for people wanting to use the code.

(2) Though the code is well-documented, I find that the paper is lacking a simple step-by-step example walking potential users through the code. Two example scripts with comments are given in the appendix, but they are, at least from my perspective, too convoluted and lengthy to be standalone. I would appreciate if the authors could add one of these examples to the main text, split into smaller segments and dressed with additional explanations.

(3) I am slightly concerned about the following: fRG is put forward as an alternative to RPA for realistic material calculations. In my opinion, the arguments brought up in the paper to support this statement are not well-founded. It seems that in the current stage of the software, the self-energy (apart from approximating it as a constant) is discarded, and bold propagators are thus replaced by bare, unrenormalized ones. Therefore, neither coherent Landau quasiparticles nor their absence seems to be captured and, for example, metal-to-insulator transitions are elusive in the implemented methods. Maybe this is not so important, as the principal goal of the fRG method in this form is the determination of order in the ground state. But even then, I have my doubts that quantitative results for real materials can be produced with the code. Assume, for example, a superconducting ground state. One would expect that it emerges from an effective attractive interaction between sufficiently long-lived quasiparticles, but, as argued above, these are not included in the current methodology. Thus, if quantitative accuracy is not the goal, what is the real advantage of fRG over RPA or FLEX approximations, which seem numerically cheaper to pursue? The authors mention that fRG provides additional screening, but not fully self-consistently and, due to the neglect of frequency dependencies, retardation effects are missing entirely. My question thus is, how much do the fRG predictions actually differ from RPA or FLEX when applied to the DFT bandstructures?

On a side note: If the Fermi surface is not renormalized by self-energy insertions the definition of the filling per site seems sketchy to me. The code is supposed to treat interacting quantum systems so the electronic density is not generally equivalent to that of the non-interacting system. Should this not be computed self-consistently at least in Hartree-Fock approximation if a constant self-energy can be included?

Requested changes

- add scaling plots and resource estimates to support claim of "high-performance"
- add step-by-step example, maybe using one of the scripts from the appendix
- revise the motivation for using the implemented fRG methods for materials

  • validity: good
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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