Ab Initio Full Cell GW+DMFT for Correlated Materials

We apply a recently introduced hybridization-flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard-model on the Bethe lattice in infinite dimensions we calculate the local two-particle-vertex for the metallic and the insulating phase. Then we go to a two-site cluster-DMFT-scheme for the two-dimensional Hubbard-model that includes short-range antiferromagnetic fluctuations and obtain the local and non-local two-particle-vertex-functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.

A cellular dynamical mean field theory approach to Mottness

We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest coupled cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.

The metal–insulator transition in the paramagnetic Hubbard Model

We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In dynamical mean-field theory (DMFT), thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as vertex corrections obtained from the two-particle impurity correlation function are included. In the presence of a nonlocal interaction, the problem may be treated within extended DMFT (EDMFT), or its diagrammatic extension, the dual boson approach. We show that here maintaining thermodynamic consistency requires knowledge of three- and four-particle impurity correlation functions, which are typically neglected. Nevertheless, the dual boson approximation to the response is remarkably close to consistency. This holds even when two-particle vertex corrections are neglected. EDMFT is consistent only in the strongly correlated regime and near half-filling, where the physics is predominantly local.

We address the problem of analytic continuation of imaginary-frequency Green's functions, which is crucial in many-body physics, using machine learning based on a multi-level residual neural network. We specifically address potential biases that can be introduced due to the use of artificially created spectral functions that are employed to train the neural network. We also implement an uncertainty estimation of the predicted spectral function, based on Monte Carlo dropout, which allows to identify frequency regions where the prediction might not be accurate, and we study the effect of noise, in particular also for situations where the noise level during training is different from that in the actual data. Our analysis demonstrates that this method can indeed achieve a high quality of prediction, comparable or better than the widely used maximum entropy method, but that further improvement is currently limited by the lack of true data that can be used for training. We also benchmark our approach by applying it to the case of SrVO$_3$, where an accurate spectral function has been obtained from dynamical mean-field theory using a solver that works directly on the real frequency axis.

The electronic structure of the rare-earth mononitrides LnN (where Ln = rare-earth), which are promising materials for future spintronics applications, is difficult to resolve experimentally due to a strong influence of defects on their transport and optical properties. At the same time, LnN are challenging for theory, since wide semiconducting 2p and 5d bands need to be described simultaneously with strongly correlated 4f states. Here, we calculate the many-body spectral functions and optical gaps of a series of LnN (with Ln = Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er) by a density-functional + dynamical mean-field theory (DFT + DMFT) approach treating the correlated Ln 4f shells within the quasi-atomic Hubbard-I approximation. The on-site Coulomb interaction in the 4f shell is evaluated by a constrained DFT + Hubbard-I approach. Furthermore, to improve the treatment of semiconducting bands in DFT + DMFT, we employ the modified Becke–Johnson semilocal exchange potential. Focusing on the paramagnetic high-temperature phase, we find that all investigated LnN are pd semiconductors with gap values ranging from 1.02 to 2.14 eV along the series. The pd band gap is direct for light Ln = La…Sm and becomes indirect for heavy rare-earths. Despite a pronounced evolution of the Ln 4f states along the series, empty 4f states are invariably found above the bottom of the 5d conduction band. The calculated spectra agree well with those available from x-ray photoemission, x-ray emission and x-ray absorption measurements.

Intermediate configurations in the plutonium and iron perovskite compound PuFeO3 are investigated using a combined density functional theory plus dynamical mean-field theory (DFT + DMFT) approach. Our findings reveal orbital-selective metal-insulator transitions driven by spin-orbit split Pu-5f states. Itinerant 5f5/2 electrons exhibit correlated metallic behavior, while localized 5f7/2 states display Mott-insulating characteristics. We report an average 5f occupancy of 4.649, suggesting intermediate valence states. Quantum mechanical analysis highlights the Pu-5f/Fe-3d hybridization, confirmed by the orbital-resolved self-energy and spectral function calculations. This study provides new insights into the electronic structure and bonding mechanisms of Pu-based perovskites, advancing the understanding of strongly correlated actinide materials.

Metal-insulator transition in correlated systems: A new numerical approach

A review of the present state of investigations of the pseudospin-electron model (PEM), which is used in the theory of strongly correlated electron systems, is given. The model is used to describe the systems with the locally anharmonic elements of structure represented in the model by pseudospins. The consideration is based on the dynamical mean field theory approach and the generalized random phase approximation. Electron spectrum and thermodynamics of the model are investigated; the cases of the simplified model, the model with strong interaction and the two-sublattice model are studied more in detail. The phase transitions into other uniform or modulated states as well as superconducting phases are described; the criteria of their realization are established. Based on this, the description of structural and dielectric (ferroelectric type) instabilities, phase separation and bistability phenomena is given. A comparison is made with the thermodynamics of the Falicov-Kimball model (which can be considered as a particular case of PEM). The possibility of applying the PEM to the analysis of thermodynamics of the real HTSC systems is discussed. Attention is paid to the unsolved problems in the study of PEM.

An acceleration of continuous time quantum Monte Carlo (CTQMC) methods is a potentially interesting branch of work as they are matchless as impurity solvers of a density functional theory in combination with a dynamical mean field theory approach for the description of electronic structures of strongly correlated materials. The inversion of the $k \times k$ matrix given by the diagram expansion order $k$ in the CTQMC update and the multiplication of the $k \times k$ matrix and the non-interacting Green's function to measure the impurity Green's function are computationally time-consuming. Here, we propose the CTQMC method in combination with a machine learning technique, which would eliminate the need for multiplication of the matrix with the non-interacting Green's function. This method predicts the accurate impurity Green's function and double occupancy at low temperature, and also considers the physical properties of high Matsubara frequency in a much shorter computational time than the conventional CTQMC method.

We study the influence of Coulomb interaction parameters on electronic structure and magnetic properties of paramagnetic bcc Fe by means of the local density approximation plus dynamical mean-field theory approach. We consider the local Coulomb interaction in the density-density form as well as in the form with spin rotational invariance approximated by averaging over all directions of the quantization axis. Our results indicate that the magnetic properties of bcc Fe are mainly affected by the Hund's rule coupling J rather than by the Hubbard U. By employing the constrained density functional theory approach in the basis of Wannier functions of spd character, we obtain U = 4 eV and J = 0.9 eV. In spite of the widespread belief that U = 4 eV is too large for bcc Fe, our calculations with the obtained values of U and J result in a satisfactory agreement with the experiment. The correlation effects caused by U are found to be weak even for large U = 6 eV. The agreement between the calculated and experimental Curie temperatures is further improved if J is reduced to 0.8 eV. However, with the decrease of J, the effective local magnetic moment moves further away from the experimental value.

Lanthanide hydrogen-rich materials have long been considered as one of the candidates with high-temperature superconducting properties in condensed matter physics, and have been a popular topic of research. Attempts to investigate the effects of different compositions of lanthanide hydrogen-rich materials are ongoing, with predictions and experimental studies in recent years showing that substances such as LaH10, CeH9, and LaH16 exhibit extremely high superconducting temperatures between 150–250 GPa. In particular, researchers have noted that, in those materials, a rise in the f orbit character at the Fermi level combined with the presence of hydrogen vibration modes at the same low energy scale will lead to an increase in the superconducting transition temperature. Here, we further elaborate on the effect of the ratios of lanthanide to hydrogen in these substances with the aim of bringing more clarity to the study of superhydrides in these extreme cases by comparing a variety of lanthanide hydrogen-rich materials with different ratios using the dynamical mean-field theory (DMFT) method, and provide ideas for later structural predictions and material property studies.

We report a study of metal-insulator transition of a strongly correlated two-band Hubbard model using a dynamical mean-field theory approach. We find that the Mott transition appears at half filling even at $T=0$ in contrast to the one-band Hubbard model. The transition is characterized by the development of a ``Kondo-like'' peak near Fermi level. We also find a signature of the coexistence of metallic and antiferromagnetic phases from the study of the single-particle Green's function and the magnetic long-range order due to the superexchange coupling between the correlated electrons. We then suggest the relevance of our results to the metal-insulator transition and the recent angle-resolved photoemission measurements of ${\mathrm{NiS}}_{2\ensuremath{-}x}{\mathrm{Se}}_{x}.$ We also study the effect of carrier doping and the comparison of our findings with the experimental results suggests the possible importance of departures from stoichiometry associated with the Se substitution. The relevance of our results to high-temperature superconductivity is also discussed.

By using the local-density approximation + dynamical mean-field theory approach, we study the low-energy electronic properties and the optical conductivity of the layered ruthenates ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. We study the interplay of spin-orbit, crystal-field, and Coulomb interactions, including the tetragonal terms of the Coulomb tensor. We show that the spin-orbit interaction is multifaced; depending on the parameter regime, filling, and temperature, it can either enhance or reduce the effective strength of correlations. We compare the results based on the two common approximations for the screened Coulomb parameters, the constrained random-phase approximation (cRPA) and the constrained local-density approximation. We show that the experimental Drude peak is better reproduced by the cRPA parameters, hinting to relatively small mass renormalizations. We find that including the spin-orbit interaction is, however, important, for a realistic description. We show that Coulomb terms with tetragonal ${D}_{4h}$ symmetry have a strong effect on the mass-enhancement anisotropy, but they do not affect sizably the total spectral function or the in-plane conductivity.