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CDMFT+HFD : an extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model

by Sarbajaya Kundu, David Senechal

Submission summary

Authors (as registered SciPost users): Sarbajaya Kundu
Submission information
Preprint Link: scipost_202312_00023v2  (pdf)
Date accepted: 2024-05-13
Date submitted: 2024-04-17 02:08
Submitted by: Kundu, Sarbajaya
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.

Author comments upon resubmission

Dear Editor,

We would like to resubmit our manuscript, titled “CDMFT+HFD: an extension for dynamical mean field theory for non-local interactions applied to the single-band extended Hubbard model”. We regret the delay in the resubmission, largely owing to the performance of some new computations.
We have responded to the questions and remarks of the referees in the space provided, and are attaching here a copy of the revised manuscript, followed by another copy of it highlighting the changes with respect to the last submitted version. Below, we list the changes made.
Apart from incorporating the suggestions of the referees, we have replaced figures 3, 4 and 7 in the manuscript by more accurate but qualitatively similar versions, and have modified the corresponding captions to include discussions on the new features in these figures. We have also performed new computations using a different method to converge the CDMFT parameters, which we chose not to use for the figures in the main text due to certain limitations, but have described in a new appendix (Appendix-B). We have also added new figures 15 and 16 to the paper, illustrating the differences between the existing fixed-point and the new Broyden method.

Thanking you,

List of changes

Let us summarize the main changes brought to the manuscript since the first version.

Changes suggested by the referees:

1. We have commented on the difficulty in finite-size scaling in our CDMFT approach in lines 153-159 of the manuscript.

2. We have added an explanation for counting the number of bath parameters for the case of the general model in the caption of Fig.2, as well as in lines 177-178.

3. The asymmetry between the orders on either side of half-filling, particularly for U=0,V=-0.4, has been addressed in the caption of Fig.7.

4. In lines 286-289, we have added a remark about the advantage of considering a general bath model along with the simple bath model, as evidenced by the change in the behaviour of the extended s-wave order as a function of filling, for increasing U.

5. In the caption of Fig. 13, we have added a remark about the prominence of the difference with and without the anomalous mean-field parameters for density in the range 0<n<0.3.

6. We have added new remarks in the final paragraph of the conclusion, in lines 398-404, about the application of our method to the single-band Hubbard model on a triangular lattice, the possibility of exploring the regime of non-perturbative repulsive local interactions and attractive non-local interactions and of including longer-range hopping terms.

7. We have replaced the term “pockets” with “regions” or “islands” everywhere it occurs in the manuscript.

Additional changes:

1. In lines 182-184, the number of bath parameters at half-filling for the general model has been changed to reflect the effectively reduced set of parameters due to the imposition of particle-hole and four-fold rotation symmetries, as opposed to the actual (larger) number used in the computations, which were mentioned in the previously submitted version. In lines 170-172, the number of bath parameters at half-filling for V<0 for the simple model increases from 6 to 10 because particle-hole symmetry is no longer imposed.

2. We have replaced figures 3, 4 and 7 in the manuscript. These have been treated with a greater accuracy and for the computations at half-filling for V<0, where phase separation occurs, the imposition of particle-hole symmetry on the bath parameters has been removed as it was in contradiction with the lack of restrictions on the corresponding mean-field parameters.The captions have been modified to include observations about the new figures, which are qualitatively similar. Correspondingly, figures 9 and 14, derived from the same data sets, have been modified for consistency.

3. We performed new computations using a different method (the Broyden method) to converge the CDMFT parameters. This is described in a new appendix (Appendix B) of the paper, and figures 15 and 16 have been added, which illustrate the differences between the results obtained using the existing fixed-point method and the Broyden method for V=-0.6 as a function of U and U=2 as a function of V<0, respectively, at half-filling. This, and point 2 above, explain the delay between the first referee reports and this new version.

Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Reports on this Submission

Anonymous Report 2 on 2024-5-4 (Invited Report)


The Authors have made a very good job in answering the questions posed the Referees. The presentation of their results and the precision of the statements made in the resubmitted manuscript have definitely improved, which will likely further enhance the paper's impact. Hence, I recommend the revised version of the manuscript by Sarbajaya Kundu and David Senechal to be published in SciPost Physics Core.


Publish (easily meets expectations and criteria for this Journal; among top 50%)

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

Anonymous Report 1 on 2024-5-1 (Invited Report)


The authors have improved consistently the manuscript, incorporating the suggestions of the two referees. Moreover, new calculations provide results with a higher accuracy and the addition of a new approach (the Broyden method) to converge the CDMFT parameters leads to a detailed, instructive analysis on the technical aspects of the CDMFT method.
I believe that the manuscript at its current version meets the expectations and criteria of SciPost Physics Core and it warrants publication in the journal.


Publish (easily meets expectations and criteria for this Journal; among top 50%)

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

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