Exact Double Counting in Combining the Dynamical Mean Field Theory and the Density Functional Theory

Electronic structure of the strongly correlated electron system plutonium hexaboride: A study from single-particle approximations and many-body calculations

The electronic structure of the strongly correlated electron system plutonium hexaboride is studied by using single-particle approximations and a many-body approach. Imaginary components of impurity Green's functions show that 5fj=5/2 and 5fj=7/2 manifolds are in conducting and insulating regimes, respectively. Quasi-particle weights and their ratio suggest that the intermediate coupling mechanism is applicable for Pu 5f electrons, and PuB6 might be in the orbital-selective localized state. The weighted summation of occupation probabilities yields the interconfiguration fluctuation and average occupation number of 5f electrons n5f ~ 5.101. The interplay of 5f-5f correlation, spin-orbit coupling, Hund's exchange interaction, many-body transition of 5f configurations, and final state effects might be responsible for the quasiparticle multiplets in electronic spectrum functions. Prominent characters in the density of state, such as the coexistence of atomic multiplet peaks in the vicinity of the Fermi level and broad Hubbard bands in the high-lying regime, suggest that PuB6 could be identified as a Racah material. Finally, the quasiparticle band structure is also presented.

Emergence of flat bands and ferromagnetic fluctuations via orbital-selective electron correlations in Mn-based kagome metal

Kagome lattice has been actively studied for the possible realization of frustration-induced two-dimensional flat bands and a number of correlation-induced phases. Currently, the search for kagome systems with a nearly dispersionless flat band close to the Fermi level is ongoing. Here, by combining theoretical and experimental tools, we present Sc3Mn3Al7Si5 as a novel realization of correlation-induced almost-flat bands in the kagome lattice in the vicinity of the Fermi level. Our magnetic susceptibility, 27Al nuclear magnetic resonance, transport, and optical conductivity measurements provide signatures of a correlated metallic phase with tantalizing ferromagnetic instability. Our dynamical mean-field calculations suggest that such ferromagnetic instability observed originates from the formation of nearly flat dispersions close to the Fermi level, where electron correlations induce strong orbital-selective renormalization and manifestation of the kagome-frustrated bands. In addition, a significant negative magnetoresistance signal is observed, which can be attributed to the suppression of flat-band-induced ferromagnetic fluctuation, which further supports the formation of flat bands in this compound. These findings broaden a new prospect to harness correlated topological phases via multiorbital correlations in 3d-based kagome systems.

Quantum critical phase of FeO spans conditions of Earth's lower mantle

Seismic and mineralogical studies have suggested regions at Earth's core-mantle boundary may be highly enriched in FeO, reported to exhibit metallic behavior at extreme pressure-temperature (P-T) conditions. However, underlying electronic processes in FeO remain poorly understood. Here we explore the electronic structure of B1-FeO at extreme conditions with large-scale theoretical modeling using state-of-the-art embedded dynamical mean field theory (eDMFT). Fine sampling of the phase diagram reveals that, instead of sharp metallization, compression of FeO at high temperatures induces a gradual orbitally selective insulator-metal transition. Specifically, at P-T conditions of the lower mantle, FeO exists in an intermediate quantum critical state, characteristic of strongly correlated electronic matter. Transport in this regime, distinct from insulating or metallic behavior, is marked by incoherent diffusion of electrons in the conducting t2g orbital and a band gap in the eg orbital, resulting in moderate electrical conductivity (~105 S/m) with modest P-T dependence as observed in experiments. Enrichment of solid FeO can thus provide a unifying explanation for independent observations of low seismic velocities and elevated electrical conductivities in heterogeneities at Earth's mantle base.

Towards near-term quantum simulation of materials

Determining the ground and excited state properties of materials is considered one of the most promising applications of quantum computers. On near-term hardware, the limiting constraint on such simulations is the requisite circuit depths and qubit numbers, which currently lie well beyond near-term capabilities. Here we develop a quantum algorithm which reduces the estimated cost of material simulations. For example, we obtain a circuit depth improvement by up to 6 orders of magnitude for a Trotter layer of time-dynamics simulation in the transition-metal oxide SrVO3 compared with the best previous quantum algorithms. We achieve this by introducing a collection of connected techniques, including highly localised and physically compact representations of materials Hamiltonians in the Wannier basis, a hybrid fermion-to-qubit mapping, and an efficient circuit compiler. Combined together, these methods leverage locality of materials Hamiltonians and result in a design that generates quantum circuits with depth independent of the system's size. Although the requisite resources for the quantum simulation of materials are still beyond current hardware, our results show that realistic simulation of specific properties may be feasible without necessarily requiring fully scalable, fault-tolerant quantum computers, providing quantum algorithm design incorporates deeper understanding of the target materials and applications.

Electron correlation and relativistic effects on the electronic properties of a plutonium and americium mixed oxide (PuAmO4): from single-particle approximation to dynamical mean-field theory

First-principles calculations were performed on a plutonium and americium mixed oxide (PuAmO4), aiming at revealing the effects of electron correlation, Pu/Am 5f-conduction electrons' hybridization, and relativity on its electronic properties. The many-body calculation suggests that the spin-orbit-coupling (SOC)-splitting of j = 5/2 and j = 7/2 manifolds are both in the weakly and moderately correlated states, respectively, implying that the jj coupling scheme is more appropriate for Pu/Am 5f electrons. The density of states, 5f occupation numbers, and Green's functions all suggest that both Pu and Am 5f electrons exhibit the coexistence of the localized and delocalized states. The admixture of 5fn atomic configurations, Pu/Am 5f-conduction electrons' hybridization, and dual characteristics of 5f electrons yield average occupation numbers of 5f electrons n5f = 4.78 and 5.86 for Pu and Am ions, respectively. Within the DFT+DMFT calculation, the weighted-summation-derived occupation numbers in terms of 5f4/5f5/5f6 and 5f5/5f6 configurations for Pu and Am 5f electrons, respectively, are in reasonable agreement with those of other DFT-based calculations.

Signature of spin-phonon coupling driven charge density wave in a kagome magnet

The intertwining between spin, charge, and lattice degrees of freedom can give rise to unusual macroscopic quantum states, including high-temperature superconductivity and quantum anomalous Hall effects. Recently, a charge density wave (CDW) has been observed in the kagome antiferromagnet FeGe, indicative of possible intertwining physics. An outstanding question is that whether magnetic correlation is fundamental for the spontaneous spatial symmetry breaking orders. Here, utilizing elastic and high-resolution inelastic x-ray scattering, we observe a c-axis superlattice vector that coexists with the 2[Formula: see text]2[Formula: see text]1 CDW vectors in the kagome plane. Most interestingly, between the magnetic and CDW transition temperatures, the phonon dynamical structure factor shows a giant phonon-energy hardening and a substantial phonon linewidth broadening near the c-axis wavevectors, both signaling the spin-phonon coupling. By first principles and model calculations, we show that both the static spin polarization and dynamic spin excitations intertwine with the phonon to drive the spatial symmetry breaking in FeGe.

Valence Fluctuation of Uranium Ions in Uranium Sesquinitride Revealed by Dynamical Mean-field Theory Merged with Density Functional Theory

The electronic properties, in particular, the occupation number of 5f electrons and the valence state of U ions in uranium sesquinitride (U2 N3 ) are studied by using density functional theory (DFT) calculations merged with dynamical mean-field theory (DMFT). The results demonstrate that j=5/2 and j=7/2 manifolds are in the weakly correlated metallic and weakly correlated insulating regimes, respectively. The quasi-particle weights indicate that LS coupling scheme is more feasible for 5f electrons, which are not in the orbital-selective localized state. The weighted summation of the occupation probabilities of 5fn (n=0,1,2,3,4) atomic configurations suggests that 5f electrons have the inter-configuration fluctuation, or the mixed-valence state for U ions, together with an average occupation number of 5f electrons n5f ∼2.234, which is in good agreement with the electron localization function (ELF) and occupation analysis based on other DFT-based calculations. The 5fn -mixing-driven inter-configuration fluctuation might originate from the dual nature of 5f electrons, and the flexible electronic configuration of U ions. Finally, the so-called quasiparticle band structure is also discussed.

Evidence of charge susceptibility and multiplef-chybridization configurations with the La doping in CeGe: a DFT + DMFT study

Kondo coupling has been extensively investigated in several Ce-based systems. However, the search for materials showing the interplay between the Kondo effect, spin-orbit interaction, and crystal-field effect along with the presence of local charge susceptibility; remains a challenge for the condensed matter community. Actually, in Ce-based systems, the strong coupling of the conduction electrons to the local magnetic moments usually hides these properties. Here, we present a detailed investigation of Ce_0.6La_0.4Ge through a combined density functional theory and dynamic mean-field theory study. Our investigations give evidence of the significant charge susceptibility and the multiple differentf-chybridization configurations. The weakening of the magnetization owing to the dilution of the Ce-site is the main cause for the appearance of such properties, which is believed to occur due to the presence of the relevant local moment andf-chybridization over the competition with the on-site Coulomb interaction.

Oxygen-Driven Enhancement of the Electron Correlation in Hexagonal Iron at Earth's Inner Core Conditions

Earth's inner core (IC) consists of mainly iron with some light elements. Understanding its structure and related physical properties has been elusive as a result of its required extremely high pressure and temperature conditions. The phase of iron, elastic anisotropy, and density-velocity deficit at the IC have long been questions of great interest. Here, we find that the electron correlation effect is enhanced by oxygen and modifies several important features, including the stability of iron oxides. Oxygen atoms energetically stabilize hexagonal-structured iron at IC conditions and induce elastic anisotropy. Electrical resistivity is much enhanced in comparison to pure hexagonal close-packed (hcp) iron as a result of the enhanced electron correlation effect, supporting the conventional thermal convection model. Moreover, our calculated seismic velocity shows a quantitative match with geologically observed preliminary reference Earth model (PREM) data. We suggest that oxygen is the essential light element to understand and model Earth's IC.

Tailoring Optical Properties in Transparent Highly Conducting Perovskites by Cationic Substitution

SrMoO₃ , SrNbO₃ , and SrVO₃ are remarkable highly conducting d¹ (V, Nb) or d² (Mo) perovskite metals with an intrinsically high transparency in the visible. A key scientific question is how the optical properties of these materials can be manipulated to make them suitable for applications as transparent electrodes and in plasmonics. Here, it is shown how 3d/4d cationic substitution in perovskites tailors the relevant materials parameters, i.e., optical transition energy and plasma frequency. With the example of the solid-state solution SrV_{1- x} Mo_x O₃ , it is shown that the absorption and reflection edges can be shifted to the edges of the visible light spectrum, resulting in a material that has the potential to outperform indium tin oxide (ITO) due to its extremely low sheet resistance. An optimum for x = 0.5, where a resistivity of 32 µΩ cm (≈12 Ω sq^-1 ) is paired with a transmittance above 84% in the whole visible spectrum is found. Quantitative comparison between experiments and electronic structure calculations show that the shift of the plasma frequency is governed by the interplay of d-band filling and electronic correlations. This study advances the knowledge about the peculiar class of highly conducting perovskites toward sustainable transparent conductors and emergent plasmonics.

Evidence of electron correlation and weak bulk plasmon in SrMoO3

We investigate the electronic structure of highly conducting perovskite SrMoO₃using valence band photoemission spectroscopy and electronic structure calculations. Large intensity corresponding to coherent feature close to Fermi level is captured by density functional theory (DFT) calculation. An additional satellite at ∼3 eV binding energy remains absent in DFT, hybrid functional (DFT-hybrid) and dynamical mean field theory (DFT + DMFT) calculations. Mo 4dspectra obtained with different surface sensitive photoemission spectroscopy suggest different surface and bulk electronic structures. DFT + DMFT spectral function is in excellent agreement with the coherent feature in the bulk Mo 4dspectra, revealing moderate electron correlation strength. A large plasmon satellite and signature of strong electron correlation are observed in the surface spectra, while the bulk spectra exhibits aweakplasmon satellite.

New Insights on the Electronic-Structural Interplay in LaPdSb and CePdSb Intermetallic Compounds

Multifunctional physical properties are usually a consequence of a rich electronic-structural interplay. To advance our understanding in this direction, we reinvestigate the structural properties of the LaPdSb and CePdSb intermetallic compounds using single-crystal neutron and X-ray diffraction. We establish that both compounds can be described by the non-centrosymmetric space group P6₃mc, where the Pd/Sb planes are puckered and show ionic order rather than ionic disorder as was previously proposed. In particular, at 300 K, the (h, k, 10)-layer contains diffuse scattering features consistent with the Pd/Sb puckered layers. The experimental results are further rationalized within the framework of DFT and DFT+ embedded DMFT methods, which confirm that a puckered structure is energetically more favorable. We also find strong correspondence between puckering strength and band topology. Namely, strong puckering removes the bands and, consequently, the Fermi surface pockets at the M point. In addition, the Pd-d band character is reduced with puckering strength. Thus, these calculations provide further insights into the microscopic origin of the puckering, especially the correspondence between the band's character, Fermi surfaces, and the strength of the puckering.

Quantum embedding theories to simulate condensed systems on quantum computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Many-Body Study of Iron(III)-Bound Human Serum Transferrin

We present the very first density functional theory and dynamical mean field theory calculations of iron-bound human serum transferrin. Peaks in the optical conductivity at 250, 300, and 450 nm were observed, in line with experimental measurements. Spin multiplet analysis suggests that the ground state is a mixed state with high entropy, indicating the importance of strong electronic correlation in this system's chemistry.

Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals

Quantum embedding is a divide and conquer strategy that aims at solving the electronic Schrödinger equation of sizeable molecules or extended systems. We establish in the present work a clearer and in-principle-exact connection between density matrix embedding theory (DMET) and density-functional theory (DFT) within the simple but nontrivial one-dimensional Hubbard model. For that purpose, we use our recent reformulation of single-impurity DMET as a Householder transformed density-matrix functional embedding theory (Ht-DMFET). On the basis of well-identified density-functional approximations, a self-consistent local potential functional embedding theory (LPFET) is formulated and implemented. Combining both LPFET and DMET numerical results with our formally exact density-functional embedding theory reveals that a single statically embedded impurity can in principle describe the density-driven Mott–Hubbard transition, provided that a complementary density-functional correlation potential (which is neglected in both DMET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work.

Thermoelectric properties plus phonon and de Haas-van Alphen frequencies of hole/electron-doped [Formula: see text]

We investigate temperature, pressure, and localization dependence of thermoelectric properties, phonon and de Haas-van Alphen (dHvA) frequencies of the anti-ferromagnetic (AFM) CeIn[Formula: see text] using density functional theory (DFT) and local, hybrid, and band correlated functionals. It is found that the maximum values of thermopower, power factor, and electronic figure of merit of this compound occur at low (high) temperatures provided that the 4f-Ce electrons are (not) localized enough. The maximum values of the thermopower, power factor, electronic figure of merit (conductivity parameters), and their related doping levels (do not) considerably depend on the localization degree and pressure. The effects of pressure on these parameters substantially depend on the degree of localization. The phonon frequencies are calculated to be real which shows that the crystal is dynamically stable. From the phonon band structure, the thermal conductivity is predicted to be homogeneous. This prediction is found consistent with the thermal conductivity components calculated along three Cartesian directions. In analogous to the thermoelectric properties, it is found that the dHvA frequencies also depend on both pressure and localization degree. To ensure that the phase transition at Néel temperature cannot remarkably affect the results, we verify the density of states (DOS) of the compound at the paramagnetic phase constructing a non-collinear magnetic structure where the angles of the spins are determined so that the resultant magnetic moment vanishes. The non-collinear results reveal that the DOS and whence the thermoelectric properties of the compound are not changed considerably by the phase transition. To validate the accuracy of the results, the total and partial DOSs are recalculated using DFT plus dynamical mean-field theory (DFT+DMFT). The DFT+DMFT DOSs, in agreement with the hybrid DOSs, predict the Kondo effect in this compound.

Exploring metastable states in UO2using hybrid functionals and dynamical mean field theory

A detailed exploration of thef-atomic orbital occupancy space for UO₂is performed using a first principles approach based on density functional theory (DFT), employing a full hybrid functional within a systematic basis set. Specifically, the PBE0 functional is combined with an occupancy biasing scheme implemented in a wavelet-based algorithm which is adapted to large supercells. The results are compared with previous DFT +Ucalculations reported in the literature, while dynamical mean field theory is also performed to provide a further base for comparison. This work shows that the computational complexity of the energy landscape of a correlatedf-electron oxide is much richer than has previously been demonstrated. The resulting calculations provide evidence of the existence of multiple previously unexplored metastable electronic states of UO₂, including those with energies which are lower than previously reported ground states.

Optical Properties of the Infinite-Layer La_{1-x}Sr_{x}NiO_{2} and Hidden Hund's Physics

We investigate the optical properties of the normal state of the infinite-layer La_{1-x}Sr_{x}NiO_{2} using density functional theory plus dynamical mean-field theory. We find a correlated metal which exhibits substantial transfer of spectral weight to high energies relative to the density functional theory. The correlations are not due to Mott physics, which would suppress the charge fluctuations and the integrated optical spectral weight as we approach a putative insulating state. Instead, we find the unusual situation, that the integrated optical spectral weight decreases with doping and increases with increasing temperature. We contrast this with the coherent component of the optical conductivity, which decreases with increasing temperature as a result of a coherence-incoherence crossover. Our studies reveal that the effective crystal field splitting is dynamical and increases strongly at low frequency. This leads to a picture of a Hund's metallic state, where dynamical orbital fluctuations are visible at intermediate energies, while at low energies a Fermi surface with primarily d_{x^{2}-y^{2}} character emerges. The infinite-layer nickelates are thus in an intermediate position between the iron based high temperature superconductors where multiorbital Hund's physics dominates and a one-band system such as the cuprates. To capture this physics we propose a low-energy two-band model with atom centered e_{g} states.

Direct observation of kink evolution due to Hund's coupling on approach to metal-insulator transition in NiS2-xSex

Understanding characteristic energy scales is a fundamentally important issue in the study of strongly correlated systems. In multiband systems, an energy scale is affected not only by the effective Coulomb interaction but also by the Hund’s coupling. Direct observation of such energy scale has been elusive so far in spite of extensive studies. Here, we report the observation of a kink structure in the low energy dispersion of NiS_2−xSe_x and its characteristic evolution with x, by using angle resolved photoemission spectroscopy. Dynamical mean field theory calculation combined with density functional theory confirms that this kink originates from Hund’s coupling. We find that the abrupt deviation from the Fermi liquid behavior in the electron self-energy results in the kink feature at low energy scale and that the kink is directly related to the coherence-incoherence crossover temperature scale. Our results mark the direct observation of the evolution of the characteristic temperature scale via kink features in the spectral function, which is the hallmark of Hund’s physics in the multiorbital system.

A decisive spectroscopic evidence of the Hund’s coupling energy scale in multi-orbital correlated systems has been lacking. Here, the authors identify a kink feature due to Hund´s coupling in the spectral function of NiS_2xSe_x as they track its evolution across the Mott-insulator transition.

Intermediate occupation numbers for 5f electrons in a Pu and U mixed oxide

In order to reveal the correlation effect on the electronic properties in particular 5f electron occupation numbers of Pu/U ions in a (Pu,U) mixed oxide-PuUO4, a first principles calculation is performed by using density functional theory (DFT) plus a dynamical mean field theory (DMFT) scheme with the spin-orbit coupling (SOC) and on-site Coulomb repulsion for correlation effect due to localized Pu/U 5f orbitals. Results demonstrate that Pu/U 5f electron occupation numbers in the ground state of PuUO4 are mainly composed of 5f4/5f5 and 5f2/5f3 configurations, and exhibiting the intermediate occupation (IO) numbers with average 5f occupation numbers of about nf = 4.879 and 2.423 for Pu and U ions, respectively, irrespective of different Pu and U lattice sites in PuUO4. Pu 5f j = 5/2 and j = 7/2 components are in moderately and weakly correlated states, respectively, while U 5f j = 5/2 and j = 7/2 manifolds are both in weakly correlated states. jj and LS coupling schemes are feasible for Pu and U 5f electrons, respectively. In order to directly compare with the experimental angle-resolved photoemission spectrum (ARPES), we also estimate the momentum-resolved electronic spectrum function for this system.

Correlation matrix renormalization theory in multi-band lattice systems

An appropriate treatment of electronic correlation effects plays an important role in accurate descriptions of physical and chemical properties of real materials. The recently proposed correlation matrix renormalization theory with sum rule correction (CMR) [1] for studying correlated-electron materials has shown good performance in molecular systems and a periodic hydrogen chain in comparison with various quantum chemistry and quantum Monte Carlo calculations [2]. This work gives a detailed formulation and computational code implementation of CMR in multi-band periodic lattice systems. This lattice CMRab initiotheory is highly efficient, has no material specific adjustable parameters, and has no double counting issues faced by the hybrid approaches like LDA +U, DFT + DMFT and DFT + GA type theories. Benchmark studies on materials with s and p orbitals in this study show that CMR in its current implementation consistently performs well for these systems as the electron correlation increases from the bonding region to the bond breaking region.

ONETEP + TOSCAM: Uniting Dynamical Mean Field Theory and Linear-Scaling Density Functional Theory

We introduce the unification of dynamical mean field theory (DMFT) and linear-scaling density functional theory (DFT), as recently implemented in ONETEP, a linear-scaling DFT package, and TOSCAM, a DMFT toolbox. This code can account for strongly correlated electronic behavior while simultaneously including the effects of the environment, making it ideally suited for studying complex and heterogeneous systems that contain transition metals and lanthanides, such as metalloproteins. We systematically introduce the necessary formalism, which must account for the nonorthogonal basis set used by ONETEP. In order to demonstrate the capabilities of this code, we apply it to carbon monoxide ligated iron porphyrin and explore the distinctly quantum-mechanical character of the iron 3d electrons during the process of photodissociation.

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

Electronic correlations in dense iron: from moderate pressure to Earth's core conditions

We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). We review in detail two particularly interesting regimes: first, a moderate pressure range up to 60 GPa and, second, the ultra-high pressure of about 360 GPa expected inside the solid inner core of Earth. Electronic correlations in iron under the moderate pressure of several tens GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced body-centered cubic α to hexagonal close-packed [Formula: see text] phase transition. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the [Formula: see text]-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in [Formula: see text]-Fe by many-electron effects; its experimental signatures are analyzed. The next section focuses on the geophysically relevant pressure-temperature regime of the Earth's inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes ([Formula: see text], [Formula: see text] and face-centered-cubic [Formula: see text]) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of [Formula: see text]-Fe and an almost perfect Fermi liquid in the case of [Formula: see text]-Fe. A recent active discussion on the electronic state and transport properties of [Formula: see text]-Fe at the EIC conditions is reviewed in details. Estimations for the dynamical many-electron contribution to the relative phase stability are presented. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework relevant for studies of iron-base systems as well as perspective directions for further development.

Benchmark of correlation matrix renormalization method in molecule calculations

We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.

Effects of correlations and temperature on the electronic structures and related physical properties of FeSi and CoSi: a comprehensive study

Here, we report detailed investigations of the temperature dependent (100-800 K) electronic structures of FeSi and CoSi by using a DFT+DMFT method where self-consistently calculated values of U and J are used. The calculated spectral functions are found to provide fairly good representation for the experimentally observed photoemission spectra for both the compounds. For FeSi, the density of states (DOS) closer to the Fermi level are found to increase with the increase in temperature up to 450 K and then they decrease, whereas, for CoSi DOS continuously decrease with an increase in temperature. The electronic states of FeSi are greatly influenced by electronic correlations while they are moderately influenced in CoSi. From momentum resolved spectral functions, the excitations have shown enhanced broadening with temperature rise in FeSi whereas an opposite behavior is observed in CoSi. In FeSi, the maximum effect of temperature on the lifetime of [Formula: see text] quasiparticles states is observed where it first decreases to 400 K and then increases, and finally becomes almost infinite at 800 K. The temperature dependent behavior of DOS and quasiparticle lifetime help us in understanding the experimentally observed electrical resistivity and Seebeck coefficient for these compounds. The calculated effective magnetic moment [Formula: see text] for Fe (∼2.5 [Formula: see text], which is closer to the experimental value) is temperature independent. The electronic structures of these compounds are showing the existence of mixed configurations with [Formula: see text] and [Formula: see text] for FeSi and CoSi, respectively. Average electrons in the d orbitals are found as  ∼6.5 and  ∼7.7 for FeSi and CoSi, respectively, with charge fluctuations [Formula: see text] 0.9 are obtained for both materials. This suggests that both the compounds are lying in the intermediate coupling regime of electronic correlations.

Correlated materials design: prospects and challenges

The design of correlated materials challenges researchers to combine the maturing, high throughput framework of DFT-based materials design with the rapidly-developing first-principles theory for correlated electron systems. We review the field of correlated materials, distinguishing two broad classes of correlation effects, static and dynamics, and describe methodologies to take them into account. We introduce a material design workflow, and illustrate it via examples in several materials classes, including superconductors, charge ordering materials and systems near an electronically driven metal to insulator transition, highlighting the interplay between theory and experiment with a view towards finding new materials. We review the statistical formulation of the errors of currently available methods to estimate formation energies. We formulate an approach for estimating a lower-bound for the probability of a new compound to form. Correlation effects have to be considered in all the material design steps. These include bridging between structure and property, obtaining the correct structure and predicting material stability. We introduce a post-processing strategy to take them into account.

Realization of continuous electron doping in bulk iron selenides and identification of a new superconducting zone

It is known that iron selenide superconductors exhibit unique characteristics distinct from iron pnictides, especially in the electron-doped region. However, a comprehensive study of continuous carrier doping and the corresponding crystal structures of FeSe is still lacking, mainly due to the difficulties in controlling the carrier density in bulk materials. Here we report the successful synthesis of a new family of bulk Lix(C3N2H10)0.37FeSe, which features a continuous superconducting dome harboring Lifshitz transition within the wide range of 0.06 ⩽ x ⩽ 0.68 . We demonstrate that with electron doping, the anion height of FeSe layers deviates linearly away from the optimized values of pnictides and pressurized FeSe. This feature leads to a new superconducting zone with unique doping dependence of the electronic structures and strong orbital-selective electronic correlation. Optimal superconductivity is achieved when the F e 3 d t 2 g orbitals have almost the same intermediate electronic correlation strength, with moderate mass enhancement between 3 ~ 4 in the two separate superconducting zones. Our results shed new light on achieving unified mechanism of superconductivity in iron-based superconductors.

Realistic estimates of superconducting properties for the cuprates: reciprocal-space diagrammatic expansion combined with variational approach

We propose a systematic approach to the systems of correlated electrons, the so-called [Formula: see text]-DE-GWF method, based on reciprocal-space ([Formula: see text]-resolved) diagrammatic expansion of the variational Gutzwiller-type wave function for parametrized models of correlated fermions. The present approach, in contrast to either variational Monte-Carlo (VMC), or the recently developed real-space diagrammatic expansion of the Gutzwiller-type wave function (direct-space DE-GWF technique), is applicable directly in the thermodynamic limit and thus is suitable for describing selected singular features of the wave-vector-dependent quantities. We employ the [Formula: see text]-DE-GWF method to extract the non-analytic part of the two leading moments of the fermion spectral-density function across the (two-dimensional) Brillouin zone for the Hubbard model and away from the half-filling. Those moments are used to evaluate the nodal quasiparticle velocities and their spectral weights in the correlated superconducting state. The two velocities determined in that manner exhibit scaling with the electron concentration qualitatively different from that obtained earlier for the excited states of the high-T _c cuprates within the projected quasi-particle ansatz, and the results are in a very good quantitative agreement with experimental data if interpreted as those characterizing the spectrum below and above the observed kink. We provide a detailed discussion of the two gaps and two excitation branches (two velocities) appearing naturally within our DE-GWF approach. The two separate sets of characteristics distinguish the renormalized quasiparticle states very close to the Fermi surface from the deeper correlated-state properties. Also, an enhancement of the [Formula: see text]-dependent magnetic susceptibility is shown to contain a spin-fluctuation contribution within our language. Finally, the [Formula: see text]-DE-GWF approach is compared to both the VMC and real-space DE-GWF results for the cases of Hubbard and t-J-U models.

Toward a predictive theory of correlated materials

Correlated electron materials display a rich variety of notable properties ranging from unconventional superconductivity to metal-insulator transitions. These properties are of interest from the point of view of applications but are hard to treat theoretically, as they result from multiple competing energy scales. Although possible in more weakly correlated materials, theoretical design and spectroscopy of strongly correlated electron materials have been a difficult challenge for many years. By treating all the relevant energy scales with sufficient accuracy, complementary advances in Green's functions and quantum Monte Carlo methods open a path to first-principles computational property predictions in this class of materials.

The effect of double counting, spin density, and Hund interaction in the different DFT+U functionals

A systematic comparative study has been performed to better understand DFT+U (density functional theory + U) method. We examine the effect of choosing different double counting and exchange-correlation functionals. The calculated energy distribution and the Hund-J dependence of potential profile for representative configurations clearly show the different behaviors of each DFT+U formalism. In particular, adopting spin-dependent exchange-correlation functionals likely leads to undesirable magnetic solution. Our analyses are further highlighted by real material examples ranging from insulating oxides (MnO and NiO) to metallic magnetic systems (SrRuO₃ and BaFe₂As₂). The current work sheds new light on understanding DFT+U and provides a guideline to use the related methods.

Phonon Softening due to Melting of the Ferromagnetic Order in Elemental Iron

We study the fundamental question of the lattice dynamics of a metallic ferromagnet in the regime where the static long-range magnetic order is replaced by the fluctuating local moments embedded in a metallic host. We use the ab initio density functional theory + embedded dynamical mean-field theory functional approach to address the dynamic stability of iron polymorphs and the phonon softening with an increased temperature. We show that the nonharmonic and inhomogeneous phonon softening measured in iron is a result of the melting of the long-range ferromagnetic order and is unrelated to the first-order structural transition from the bcc to the fcc phase, as is usually assumed. We predict that the bcc structure is dynamically stable at all temperatures at normal pressure and is thermodynamically unstable only between the bcc-α and the bcc-δ phases of iron.

Localized-itinerant dichotomy and unconventional magnetism in SrRu2O6

Electron correlations tend to generate local magnetic moments that usually order if the lattices are not too frustrated. The hexagonal compound SrRu₂O₆ has a relatively high Neel temperature but small local moments, which seem to be at odds with the nominal valence of Ru⁵⁺ in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{2g}^{3}$$\end{document}t2g3 configuration. Here, we investigate the electronic property of SrRu₂O₆ using density functional theory (DFT) combined with dynamical-mean-field theory (DMFT). We find that the strong hybridization between Ru d and O p states results in a Ru valence that is closer to +4, leading to the small ordered moment ~1.2 μ_B. While this is consistent with a DFT prediction, correlation effects are found to play a significant role. The local moment per Ru site remains finite ~2.3 μ_B in the whole temperature range investigated. Due to the lower symmetry, the t_2g manifold is split and the quasiparticle weight is renormalized significantly in the a_1g state, while the renormalization in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${e}_{g}^{{\rm{^{\prime} }}}$$\end{document}eg′ states is about a factor of 2–3 weaker. Our theoretical Neel temperature ~700 K is in reasonable agreement with experimental observations. SrRu₂O₆ is a unique system in which localized and itinerant electrons coexist with the proximity to an orbitally-selective Mott transition within the t_2g sector.

Mott Transition and Magnetism in Rare Earth Nickelates and its Fingerprint on the X-ray Scattering

The metal-insulator transition (MIT) remains among the most thoroughly studied phenomena in solid state physics, but the complexity of the phenomena, which usually involves cooperation of many degrees of freedom including orbitals, fluctuating local moments, magnetism, and the crystal structure, have resisted predictive ab-initio treatment. Here we develop ab-initio theoretical method for correlated electron materials, based on Dynamical Mean Field Theory, which can predict the change of the crystal structure across the MIT at finite temperature. This allows us to study the coupling between electronic, magnetic and orbital degrees of freedom with the crystal structure across the MIT in rare-earth nickelates. We predict the electronic free energy profile of the competing states, and the theoretical magnetic ground state configuration, which is in agreement with neutron scattering data, but is different from the magnetic models proposed before. The resonant elastic X-ray response at the K-edge, which was argued to be a probe of the charge order, is theoretically modelled within the Dynamical Mean Field Theory, including the core-hole interaction. We show that the line-shape of the measured resonant elastic X-ray response can be explained with the “site-selective” Mott scenario without real charge order on Ni sites.

Dynamical screening in correlated electron systems-from lattice models to realistic materials

Recent progress in treating the dynamical nature of the screened Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of these schemes to U-V Hubbard models and correlated materials.

Free Energy from Stationary Implementation of the DFT+DMFT Functional

The stationary functional of the density functional plus embedded dynamical mean field theory formalism to perform free energy calculations and structural relaxations is implemented for the first time. Here, the first order error in the density leads to a much smaller, second order error in the free energy. The method is applied to several well-known correlated materials: metallic SrVO_{3}, Mott insulating FeO, and elemental cerium, to show that it predicts the lattice constants with good accuracy. In cerium, we show that our method predicts the isostructural transition between the α and γ phases, and resolve the long-standing controversy in the driving mechanism of this transition.