Full d-manifold DMFT with numerically exact solvers has remained computationally prohibitive for spin-orbit materials due their scaling and severe sign problem, forcing the community to rely on simplified one- and three-band models that omit the e_g states despite their proximity with the t_2g orbitals. We present the first full five-orbital Dynamical Mean-Field Theory (DMFT) calculations including spin-orbit coupling for the layered iridates and rhodates and , revealing that the correlation effects shift significantly the e_g states through static mean-field corrections rather than dynamical fluctuations. Motivated by this insight, we introduce hybrid-DMFT (hDMFT), which treats these orbitals and their coupling to the low-energy manifold at the mean-field level while maintaining near quantitative accuracy at a drastically reduced computational cost. These calculation establish hDMFT as a practical and accurate method for full d-manifold studies of layered iridates and rhodates, enabling systematic investigations of temperature, doping and pressure dependence that were previously computationally intractable.

As a consequence of their spin-orbit entangled ground state, many 5d^5 iridate materials display a peculiar double peak structure in optical transport quantities, such as absorption and conductivity. Their common interpretation is based on the presence of Hubbard subbands in the half-filled j_eff=1/2 manifold. Herein, we challenge this picture, proposing a scenario based on the presence of spin-polaron (SP) quasiparticles, and assigning a dominant SP character to the first peak. We illustrate it by taking the materials Ba_2IrO_4 and Sr_2IrO_4 as paradigmatic examples, which we investigate within the dynamical mean-field theory and the self-consistent Born approximation. Both theories reproduce nontrivial features revealed by angle-resolved photoemission spectroscopy and optical transport measurements, supporting our interpretation. In the case of Sr_2IrO_4, we show how the SP scenario survives in the low-doped regime. Similar optical transport fingerprints are expected to be found in the wider class of 5d^5 iridates and more generally in strongly correlated antiferromagnetic regimes, such as those found in cuprates.

In the quest of new exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled $j_{\mathrm{eff}}=1/2$ ground state have been in the spotlight in recent years. Also in view of parallels with the low-energy physics of high-temperature superconducting cuprates, the validity of a single- or few-band picture in terms of the $j_{\mathrm{eff}}$ states is key. However, in particular for its structurally simple member Ba$_2$IrO$_4$, such a systematic construction and subsequent analysis of minimal low-energy models are still missing. Here we show by means of a combination of different ab initio techniques with dynamical mean-field theory that a three-band model in terms of Ir-$j_{\mathrm{eff}}$ states fully retains the low-energy physics of the system as compared to a full Ir-$5d$ model. Providing a detailed study of the three-band model in terms of spin-orbit coupling, Hund's coupling and Coulomb interactions, we map out a rich phase diagram and identify a region of effective one-band metal-insulator transition relevant to Ba$_2$IrO$_4$. Compared to available angle-resolved photoemission spectra, we find good agreement of salient aspects of the calculated spectral function and identify features which require the inclusion of non-local fluctuations. In a broader context, we envisage the three- and five-band models developed in this study to be relevant for the study of doped Ba$_2$IrO$_4$ and to clarify further the similarities and differences with cuprates.

In quantum chemistry, single-reference Coupled Cluster theory, and its refinements introduced by Bartlett, has become a "gold-standard" predictive method for taking into account electronic correlations in molecules. In this article, we introduce a new formalism based on a Coupled Cluster expansion of the wave function that is suited to describe model periodic systems and apply this methodology to the case of hole-doped antiferromagnetic two-dimensional (2D)-square spin-lattices as a proof of concept. More precisely, we focus our study on 1/5 and 1/7 doping ratios and discuss the possible ordering effect due to large hole-hole repulsion. Starting from one of the equivalent single determinants exhibiting a full spin alternation and the most remote location of the holes as a single reference, the method incorporates some corrections to the traditional Coupled Cluster formalism to take into account the nonadditivity of excitation energies to multiply excited determinants. The amplitudes of the excitations, which are possible on the excited determinants but impossible on the reference, are evaluated perturbatively, while their effect is treated as a dressing in the basic equations. The expansion does not show any sign of divergence of the wave operator. Finally, the probabilities of holes moving toward the first- and second-neighboring sites are reported, which confirms the importance of the hole-hole repulsion and offers a picture of how stripes expand around its central line in the "stripe phases" observed in cuprates.

Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.

We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant (independent of the system volume) and algebraically vanishing (scaling as an inverse power law with the system volume) boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

5d iridium oxides are of huge interest due to the potential for new quantum states driven by strong spin-orbit coupling. The strontium iridate Sr_{2}IrO_{4} is particularly in the spotlight because of the so-called j_{eff}=1/2 state consisting of a quantum superposition of the three local t_{2g} orbitals with, in its simplest version, nearly equal populations, which stabilizes an unconventional Mott insulating state. Here, we report an anisotropic and aspherical magnetization density distribution measured by polarized neutron diffraction in a magnetic field up to 5 T at 4 K, which strongly deviates from a local j_{eff}=1/2 picture even when distortion-induced deviations from the equal weights of the orbital populations are taken into account. Once reconstructed by the maximum entropy method and multipole expansion model refinement, the magnetization density shows four cross-shaped positive lobes along the crystallographic tetragonal axes with a large spatial extent, showing that the xy orbital contribution is dominant. The analogy to the superconducting copper oxide systems might then be weaker than commonly thought.

${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ is characterized by a large spin-orbit coupling, which gives rise to bands with strongly entangled spin and orbital characters, called ${\mathrm{J}}_{1/2}$ and ${\mathrm{J}}_{3/2}$. We use light-polarization dependent ARPES to study directly the orbital character of these bands and fully map out their dispersion. We observe bands in very good agreement with our cluster dynamical mean-field theory calculations. We show that the ${\mathrm{J}}_{1/2}$ band, the closest to the Fermi level ${E}_{F}$, is dominated by ${d}_{xz}$ character along ${k}_{x}$ and ${d}_{yz}$ along ${k}_{y}$. This is actually in agreement with an isotropic ${\mathrm{J}}_{1/2}$ character on average, but this large orbital dependence in $\mathbf{k}$ space was mostly overlooked before. It gives rise to strong modulations of the ARPES intensity that we explain and carefully take into account to compare dispersions in equivalent directions of the Brillouin zone. Although the latter dispersions look different at first, suggesting possible symmetry breakings, they are found essentially similar, once corrected for these intensity variations. In particular, the pseudogaplike features close to the $X$ point appearing in the nearly metallic 15% Rh-doped ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ strongly depend on experimental conditions. We reveal that there is nevertheless an energy scale of 30 meV below which spectral weight is suppressed, independent of the experimental conditions, which gives a reliable basis to analyze this behavior. We suggest it is caused by disorder.

The spin-orbit Mott insulator Sr2IrO4 has attracted a lot of interest in recent years from theory and experiment due to its close connection to isostructural high-temperature copper oxide superconductors. Despite not being superconductive, its spectral features closely resemble those of the cuprates, including Fermi surface and pseudogap properties. In this article, we review and extend recent work in the theoretical description of the spectral function of pure and electron-doped Sr2IrO4 based on a cluster extension of dynamical mean-field theory ('oriented-cluster DMFT') and compare it to available angle-resolved photoemission data. Current theories provide surprisingly good agreement for pure and electron-doped Sr2IrO4, both in the paramagnetic and antiferromagnetic phases. Most notably, one obtains simple explanations for the experimentally observed steep feature around the M point and the pseudo-gap-like spectral feature in electron-doped Sr2IrO4.

Cyril Martins, ∗ Benjamin Lenz, ∗ Luca Perfetti, Veronique Brouet, François Bertran, and Silke Biermann 6, † Laboratoire de Chimie et Physique Quantiques, UMR 5626, Université Paul Sabatier, 118 route de Narbonne, 31400 Toulouse, France Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644, Université Paris-Saclay, 91128 Palaiseau, France Laboratoire des Solides Irradiés, Ecole Polytechnique, CNRS, CEA, Université Paris-Saclay, 91128 Palaiseau, France Laboratoire de Physique des Solides, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin-BP 48, 91192 Gif sur Yvette, France Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France (Dated: August 12, 2018)

We address the role of non-local Coulomb correlations and short-range magnetic fluctuations in the high-temperature phase of Sr$_2$IrO$_4$ within state-of-the-art spectroscopic and first-principles theoretical methods. Introducing a novel cluster dynamical mean field scheme, we compute momentum-resolved spectral functions, which we find to be in excellent agreement with angle-resolved photoemission spectra. We show that while short-range antiferromagnetic fluctuations are crucial to account for the electronic properties of the material even in the high-temperature paramagnetic phase, long-range magnetic order is not a necessary ingredient of the insulating state. Upon doping, an exotic metallic state is generated, exhibiting cuprate-like pseudo-gap spectral properties, for which we propose a surprisingly simple theoretical mechanism.

The interplay of spin-orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin-orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr2IrO4) and its 4d metallic counterpart, strontium rhodate (Sr2RhO4). While a Mott-insulating state is obtained for Sr2IrO4 in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr2RhO4 show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin-orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin-orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d1 perovskites.

Motivated by recent spin- and angular-resolved photoemission (SARPES) measurements of the two-dimensional electronic states confined near the (001) surface of oxygen-deficient SrTiO_{3}, we explore their spin structure by means of ab initio density functional theory (DFT) calculations of slabs. Relativistic nonmagnetic DFT calculations display Rashba-like spin winding with a splitting of a few meV and when surface magnetism on the Ti ions is included, bands become spin-split with an energy difference ∼100  meV at the Γ point, consistent with SARPES findings. While magnetism tends to suppress the effects of the relativistic Rashba interaction, signatures of it are still clearly visible in terms of complex spin textures. Furthermore, we observe an atomic specialization phenomenon, namely, two types of electronic contributions: one is from Ti atoms neighboring the oxygen vacancies that acquire rather large magnetic moments and mostly create in-gap states; another comes from the partly polarized t_{2g} itinerant electrons of Ti atoms lying further away from the oxygen vacancy, which form the two-dimensional electron system and are responsible for the Rashba spin winding and the spin splitting at the Fermi surface.

We present the TRIQS/DFTTools package, an application based on the TRIQS library that connects this toolbox to realistic materials calculations based on density functional theory (DFT). In particular, TRIQS/DFTTools together with TRIQS allows an efficient implementation of DFT plus dynamical mean-field theory (DMFT) calculations. It supplies tools and methods to construct Wannier functions and to perform the DMFT self-consistency cycle in this basis set. Post-processing tools, such as band-structure plotting or the calculation of transport properties are also implemented. The package comes with a fully charge self-consistent interface to the Wien2k band structure code, as well as a generic interface that allows to use TRIQS/DFTTools together with a large variety of DFT codes. It is distributed under the GNU General Public License (GPLv3).

We discuss the notions of spin-orbital polarization and ordering in paramagnetic materials, and address their consequences in transition metal oxides. Extending the combined density functional and dynamical mean field theory scheme to the case of materials with large spin-orbit interactions, we investigate the electronic excitations of the paramagnetic phases of Sr2IrO4 and Sr2RhO4. We show that the interplay of spin-orbit interactions, structural distortions and Coulomb interactions suppresses spin-orbital fluctuations. As a result, the room temperature phase of Sr2IrO4 is a paramagnetic spin-orbitally ordered Mott insulator. In Sr2RhO4, the effective spin-orbital degeneracy is reduced, but the material remains metallic, due to both, smaller spin-orbit and smaller Coulomb interactions. We find excellent agreement of our ab-initio calculations for Sr2RhO4 with angle-resolved photoemission, and make predictions for spectra of the paramagnetic phase of Sr2IrO4.

We discuss the notions of spin-orbital polarization and ordering in paramagnetic materials, and address their consequences in transition-metal oxides. Extending the combined density functional and dynamical mean field theory scheme to the case of materials with large spin-orbit interactions, we investigate the electronic excitations of the paramagnetic phases of Sr(2)IrO(4) and Sr(2)RhO(4). We show that the interplay of spin-orbit interactions, structural distortions and Coulomb interactions suppresses spin-orbital fluctuations. As a result, the room temperature phase of Sr(2)IrO(4) is a paramagnetic spin-orbitally ordered Mott insulator. In Sr(2)RhO(4), the effective spin-orbital degeneracy is reduced, but the material remains metallic, due to both, smaller spin-orbit and smaller Coulomb interactions. The corresponding spectra are in excellent agreement with photoemission data. Finally, we make predictions for the spectra of paramagnetic Sr(2)IrO(4).

Cette these s'interesse a l'interaction entre le couplage spin-orbite et les correlations electroniques dans la matiere condensee. En effet, de plus en plus de materiaux - tels que les isolants topologiques ou les oxydes de metaux de transition 5d a base d'iridium - presentent des proprietes pour lesquels l'interaction spin-orbite joue un role essentiel. Parmi eux, l'iridate de strontium (Sr2IrO4) a recemment ete decrit comme un de Mott regi par les effets spin-orbite: dans cette image, l'interaction de Coulomb entre les electrons et le couplage spin-orbite se combinent pour rendre le compose isolant. Nous avons etudie la phase isolante paramagnetique de ce materiau avec l'approche LDA+DMFT, une methode qui combine la theorie de la fonctionnelle de la densite dans l'approximation de la densite locale (LDA) avec la theorie du champ moyen dynamique (DMFT). Sr2IrO4 s'est avere etre un isolant de Mott pour une valeur raisonnable des correlations electroniques une fois que le couplage spin-orbite et les distorsions structurales du cristal ont ete pris en compte. En outre, nos resultats mettent en evidence les roles respectifs joues par ces deux elements dans l'obtention d'un etat isolant et montrent que seule leur action conjointe permet d'ouvrir un gap de Mott dans un tel compose. Afin de realiser cette etude, le couplage spin-orbite a du etre inclus au sein du formalisme LDA+DMFT. L'interet d'un tel developpement technique depasse le cas de Sr2IrO4, cette implementation, dite LDA+SO+DMFT, pouvant etre aussi utilisee pour prendre en compte les correlations electroniques dans d'autres oxydes de metaux de transition 5d ou meme au sein des isolants topologiques