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Formation of CuO$_2$ sublattices by suppression of interlattice correlations in tetragonal CuO
by Max Bramberger, Benjamin BacqLabreuil, Martin Grundner, Silke Biermann, Ulrich Schollwöck, Sebastian Paeckel, Benjamin Lenz
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Submission summary
Authors (as registered SciPost users):  Benjamin BacqLabreuil · Max Bramberger · Benjamin Lenz 
Submission information  

Preprint Link:  scipost_202205_00016v1 (pdf) 
Date submitted:  20220518 11:52 
Submitted by:  Bramberger, Max 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We investigate the tetragonal phase of the binary transition metal oxide CuO (tCuO) within the context of cellular dynamical meanfield theory. Due to its strong antiferromagnetic correlations and simple structure, analysing the physics of tCuO is of high interest as it may pave the way towards a more complete understanding of high temperature superconductivity in holedoped antiferromagnets. In this work we give a formal justification for the weak coupling assumption that has previously been made for the interconnected sublattices within a single layer of tCuO by studying the nonlocal selfenergies of the system. We compute momentumresolved spectral functions using a Matrix Product State (MPS)based impurity solver directly on the real axis, which does not require any numerically illconditioned analytic continuation. The agreement with photoemission spectroscopy indicates that a single band Hubbard model is sufficient to capture the material's low energy physics. We perform calculations on a range of different temperatures, finding two magnetic regimes, for which we identify the driving mechanism behind their respective insulating state. Finally, we show that in the holedoped regime the sublattice structure of tCuO has interesting consequences on the symmetry of the superconducting state.
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Anonymous Report 2 on 202286 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202205_00016v1, delivered 20220806, doi: 10.21468/SciPost.Report.5505
Strengths
Stateoftheart numerical technology
Weaknesses
Discussion of previous literature on CDMFT on copper oxide planes should be improved
Report
The manuscript investigates the physics of copperoxide layers in the framework of dynamical meanfield theory. Due to numerical advances, the authors can achieve unprecedented precision in simulating Green's functions, which are the central object in DMFT. Thereby, the authors argue that the two sublattices in the copperoxide planes are only weakly coupled and an effective description of the system as a single band Hubbard model is justified. The simulation clusters are coupled to a large number of bath sites, such that the simulations are far beyond the reach of Exact Diagonalization approaches. The possibility to evaluate Greens functions directly on the real axis is very exciting and an important step forward for dynamical meanfield theory. This advance is facilitated by modern and stateoftheart matrix product state techniques for zero temperature as well as Quantum Monte Carlo simulations at finite temperature.
The manuscript is well written and also the explanations of numerical techniques is thorough, which will be of great benefit to future users of this technique. My main criticism of the manuscript is the results have not been properly put into context with previous literature. Given the wide range of literature on the topic, the novelty of all physical results obtained in the manuscript cannot fully be claimed. Therefore, The authors need to thoroughly discuss, which of the results had already been attained in previous studies and where the methodological advances surpass the literature. As presented, it seems as if all results are completely new, which is not entirely the case.
The authors mention stripe order, and sketch it in Fig. 1c). However, it is not immediately clear what they mean by this. Does stripe order refer to a combined charge and spin ordering or is it just referring to a stripy antiferromagnet, breaking lattice rotation symmetry without charge ordering? This should be explained in more detail.
Apart from these criticisms which should be addressed, I can recommend the publication of the manuscript in SciPost.
Author: Max Bramberger on 20220912 [id 2805]
(in reply to Report 2 on 20220806)
We thank the referee for reviewing our work and for the positive feedback. In the following we will address the points of concern raised by the referee.
The manuscript is well written and also the explanations of numerical techniques is thorough, which will be of great benefit to future users of this technique. My main criticism of the manuscript is the results have not been properly put into context with previous literature. Given the wide range of literature on the topic, the novelty of all physical results obtained in the manuscript cannot fully be claimed. Therefore, The authors need to thoroughly discuss, which of the results had already been attained in previous studies and where the methodological advances surpass the literature. As presented, it seems as if all results are completely new, which is not entirely the case.
We thank the referee for pointing this out. In order to address this point, we made several corrections throughout the manuscript to better situate our work with regard to the existing literature:
 In Sec. 3.1, the citations referring to the framework of cluster dynamical meanfield theory (CDMFT) have been updated, and references to relevant studies using CDMFT in the context of cuprates were added. We also recall the specificity of the $2\times2$ cluster when presenting the block construction by citing a set of important studies.
 In Sec. 3.2, we now make clear that CDMFT has been used previously to study the spectral properties of cuprates in comparison to experiments, but that it is the first time that this technique is applied to tCuO. Moreover, we specify that the lowenergy spinpolaron interpretation is not new and we refer to relevant works on this topic.
 In Sec 3.3, the interpretation of the frequency suppression of the selfenergy at low temperatures has been slightly modified so to show the connection to prior works. Concerning the momentum differentiation in the paramagnetic regime, references to previous studies discussing this topic using quantum cluster methods were also added.
 In Sec. 4, the citations referring to the framework of CDMFT have been updated.
The authors mention stripe order, and sketch it in Fig. 1c). However, it is not immediately clear what they mean by this. Does stripe order refer to a combined charge and spin ordering or is it just referring to a stripy antiferromagnet, breaking lattice rotation symmetry without charge ordering? This should be explained in more detail.
In order to make the kind of stripe order that we are addressing clearer we added a few sentences to Sec.1 stating that we study a columnar magnetic order corresponding to an ordering vector $Q=(0, \pi)$ and refer to it as magnetic stripe order. We furthermore added a similar remark to the caption of Fig.1. In addition we added a sentence clarifying that we did not study charge ordered stripes.
Apart from these criticisms which should be addressed, I can recommend the publication of the manuscript in SciPost.
We hope that our changes fully address the criticisms raised by the referee and that our manuscript can now be recommended for publication.
Anonymous Report 1 on 2022726 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202205_00016v1, delivered 20220726, doi: 10.21468/SciPost.Report.5452
Report
In their manuscript ''Formation of CuO2 sublattices by suppression of interlattice correlations in tetragonal CuO" the authors investigate the tetragonal phase of the binary transition metal oxide CuO using cellular dynamical meanfield theory for finite temperatures as well as for T=0. The main result of the paper is that the intersublattice hopping $t_d$ can be treated perturbatively. The authors show that their results are in good agreement with ARPES experiments and that those systems can be seen as good candidates to be described by a singleband Hubbard model. The authors also investigate magnetic ordering, as well as superconducting properties in the system at finite temperatures.
The paper is clearly written, the calculations for T=0, as well as finite temperatures are well described and also comparisons between the two methods are shown. Some pertinent point, however, still needs some further clarification, before I am able to recommend the publication:
In Fig. 2 the authors show the selfenergies of the onsite (a), intralattice hopping (b) and interlattice hopping (c) for zero temperature. It is well shown, that for T=0 the selfenergy Sigma_{t_d} can be neglected in comparison to the onsite and intralattice selfenergy. Since the approximation of Sigma_{t_d} being small is then used throughout the paper to create the socalled "block construction", also for finite temperature calculations, I ask the authors if they looked at the temperature dependence of
Sigma_{loc}[n=0] /  \Sigma_{t_d}[n=0]
Sigma_{t}[n=0] /  \Sigma_{t_d}[n=0]
Author: Max Bramberger on 20220912 [id 2806]
(in reply to Report 1 on 20220726)
In their manuscript Formation of CuO2 sublattices by suppression of interlattice correlations in tetragonal CuO the authors investigate the tetragonal phase of the binary transition metal oxide CuO using cellular dynamical meanfield theory for finite temperatures as well as for T=0. The main result of the paper is that the intersublattice hopping $t_d$ can be treated perturbatively. The authors show that their results are in good agreement with ARPES experiments and that those systems can be seen as good candidates to be described by a singleband Hubbard model. The authors also investigate magnetic ordering, as well as superconducting properties in the system at finite temperatures.
The paper is clearly written, the calculations for $T=0$, as well as finite temperatures are well described and also comparisons between the two methods are shown. Some pertinent point, however, still needs some further clarification, before I am able to recommend the publication:
We thank the referee for reviewing our work and for the positive feedback. In the following we address the pertinent point mentioned by the referee.
In Fig. 2 the authors show the selfenergies of the onsite (a), intralattice hopping (b) and interlattice hopping (c) for zero temperature. It is well shown, that for T=0 the selfenergy $\Sigma_{t_d}$ can be neglected in comparison to the onsite and intralattice selfenergy. Since the approximation of $\Sigma_{t_d}$ being small is then used throughout the paper to create the socalled block construction, also for finite temperature calculations, I ask the authors if they looked at the temperature dependence of \begin{align} \Sigma_\textrm{loc}[n=0] /  \Sigma_{t_d}[n=0]\newline \Sigma_{t}[n=0] /  \Sigma_{t_d}[n=0] \end{align}
We thank the referee for this important remark. We did indeed also investigate the temperature dependence of $\Sigma_\textrm{loc}[n=0] /  \Sigma_{t_d}[n=0]$ and $\Sigma_{t}[n=0] /  \Sigma_{t_d}[n=0]$. Our finding is that the decoupling of tCuO into two CuO2 sublattices happens at all temperatures we studied, irrespective of magnetic ordering. We added a remark to Sec.3.1 together with a figure in the appendix showing the temperature dependence of $\Sigma_\textrm{loc}[n=0] /  \Sigma_{t_d}[n=0]$ and $\Sigma_{t}[n=0] /  \Sigma_{t_d}[n=0]$.
We think that our changes address the point that the referee mentioned and hope that he/she can recommend the current version of our manuscript for publication in SciPost Physics.
Anonymous on 20220726 [id 2688]
In their manuscript ''Formation of CuO2 sublattices by suppression of interlattice correlations in tetragonal CuO" the authors investigate the tetragonal phase of the binary transition metal oxide CuO using cellular dynamical meanfield theory for finite temperatures as well as for T=0. The main result of the paper is that the intersublattice hopping $t_d$ can be treated perturbatively. The authors show that their results are in good agreement with ARPES experiments and that those systems can be seen as good candidates to be described by a singleband Hubbard model. The authors also investigate magnetic ordering, as well as superconducting properties in the system at finite temperatures.
The paper is clearly written, the calculations for T=0, as well as finite temperatures are well described and also comparisons between the two methods are shown. Some pertinent point, however, still needs some further clarification, before I am able to recommend the publication:
In Fig. 2 the authors show the selfenergies of the onsite (a), intralattice hopping (b) and interlattice hopping (c) for zero temperature. It is well shown, that for T=0 the selfenergy Sigma_{t_d} can be neglected in comparison to the onsite and intralattice selfenergy. Since the approximation of Sigma_{t_d} being small is then used throughout the paper to create the socalled "block construction", also for finite temperature calculations, I ask the authors if they looked at the temperature dependence of
Sigma_{loc}[n=0] /  \Sigma_{t_d}[n=0]
Sigma_{t}[n=0] /  \Sigma_{t_d}[n=0]
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