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

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,
Sincerely,
Authors.

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.