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Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures

by D. Rohe, C. Honerkamp

Submission summary

As Contributors: Daniel Rohe
Arxiv Link:
Date submitted: 2020-05-05
Submitted by: Rohe, Daniel
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission 2005.00827v1 on 5 May 2020

Reports on this Submission

Report 1 by Walter Metzner on 2020-5-27 Invited Report


The authors present a one-loop functional renormalization group (fRG) study of the two-dimensional half-filled Hubbard model at finite temperature, with a focus on the frequency-dependence of the self-energy. Using a static approximation for the two-particle vertex, the flow of the self-energy can be computed directly on the real frequency axis. While numerous fRG studies of the Hubbard model have already been published, there are only few results for the real-frequency self-energy.

The authors observe an unconventional dip of the imaginary part of the self-energy around zero frequency, which is present only at finite temperature.This feature was discovered previously within plain second order perturbation theory (as the authors correctly point out), but it didn't receive the attention it deserves. They thoroughly discuss the consequences of the dip for the spectral function and Fermi liquid behavior. Signatures of pseudogap behavior are also discussed.

I recommend publication after the points under ''Requested changes'' have been taken into account.

Requested changes

I see several points that should or could be improved, which I divide in ''mandatory'' and ''optional''.


1) The thermal dip in the self-energy was observed already by Katanin and Kampf in their fRG study (Refs. 31 and 32). Their work and a comparison to their results should be discussed more thoroughly.

2) In 1.2 it is claimed that Ref. 16 is the only fRG implementation where the self-energy is computed directly on the real axis. This may be true for studies of the 2D Hubbard model, but certainly not in general. Hence, the authors should restrict the statement to the two-dimensional Hubbard model.

3) In the introduction the authors write that ''qualitatively there are hardly any issues'' (for the 2D Hubbard model). This is not true and should therefore be removed. In particular, none of the existing fRG versions is able to capture the pseudogap, and no method at all is able to deal with strange metal transport behavior.

4) The authors should not try to sell a one-loop truncation with a static vertex as a step toward ''quantitative maturity'' (in introduction), as it is clear that higher loops and frequency dependencies of the vertex change results a lot already at moderate interaction strength. The partial agreement with results from more accurate methods might be just accidental.


1) I strongly encourage the authors to include results away from half-filling in the present paper, instead of postponing this to a future publication. This would allow one to assess to what extent the unusual self-energy dip is associated with nesting and the van Hove singularity. It shouldn't be hard to produce the data and add a few figures. The method remains the same, so that the paper would not become much longer.

Minor points and typos:

1) There are words missing in the last sentence of the first paragraph on page 3.

2) Why do the authors refer to their results in Fig. 1 as ``raw data''? What does it mean?

3) There is something missing in the condition ''omega = ...'' in line 11 on page 6. As written, the equation doesn't make sense.

4) ''FEA'' is an unusual acronym for the fluctuation-exchange approximation. Why not ''FLEX'', which is the standard one?

5) I don't see the QMC data points from Rost 2012 in Fig. 4. Were they forgotten?

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

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