# Formation of CuO$_2$ sublattices by suppression of interlattice correlations in tetragonal CuO

### Submission summary

 As Contributors: Benjamin Bacq-Labreuil · Max Bramberger · Benjamin Lenz Preprint link: scipost_202205_00016v1 Date submitted: 2022-05-18 11:52 Submitted by: Bramberger, Max Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Condensed Matter Physics - Computational Approaches: Theoretical, Computational

### Abstract

We investigate the tetragonal phase of the binary transition metal oxide CuO (t-CuO) within the context of cellular dynamical mean-field theory. Due to its strong antiferromagnetic correlations and simple structure, analysing the physics of t-CuO is of high interest as it may pave the way towards a more complete understanding of high temperature superconductivity in hole-doped 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 t-CuO by studying the non-local self-energies of the system. We compute momentum-resolved spectral functions using a Matrix Product State (MPS)-based impurity solver directly on the real axis, which does not require any numerically ill-conditioned 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 hole-doped regime the sublattice structure of t-CuO has interesting consequences on the symmetry of the superconducting state.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_202205_00016v1 on 18 May 2022

## Reports on this Submission

### Strengths

State-of-the-art numerical technology

### Weaknesses

Discussion of previous literature on CDMFT on copper oxide planes should be improved

### Report

The manuscript investigates the physics of copper-oxide layers in the framework of dynamical mean-field 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 copper-oxide 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 mean-field theory. This advance is facilitated by modern and state-of-the-art 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.

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

### 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 mean-field theory for finite temperatures as well as for T=0. The main result of the paper is that the inter-sublattice 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 single-band 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 self-energies of the onsite (a), intra-lattice hopping (b) and inter-lattice hopping (c) for zero temperature. It is well shown, that for T=0 the self-energy Sigma_{t_d} can be neglected in comparison to the onsite and intra-lattice self-energy. Since the approximation of Sigma_{t_d} being small is then used throughout the paper to create the so-called "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]|

### Attachment

• validity: high
• significance: high
• originality: ok
• clarity: top
• formatting: excellent
• grammar: perfect

### Anonymous on 2022-07-26  [id 2688]

Category:
question

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 mean-field theory for finite temperatures as well as for T=0. The main result of the paper is that the inter-sublattice 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 single-band 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 self-energies of the onsite (a), intra-lattice hopping (b) and inter-lattice hopping (c) for zero temperature. It is well shown, that for T=0 the self-energy Sigma_{t_d} can be neglected in comparison to the onsite and intra-lattice self-energy. Since the approximation of Sigma_{t_d} being small is then used throughout the paper to create the so-called "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]|