There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly{correlated materials where the one{electron description breaks down. We illustrate the method with several examples where interactions play a dominant role: systems near metal{insulator transition, systems near volume collapse transition, and systems with local moments.

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Electronic structure calculations with dynamical mean-field theory

https://ralphgroup.lassp.cornell.edu/papers/JMMM-320-1190-2008.pdf

Spin transfer torques

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Density functional theory for transition metals and transition metal chemistry

Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. We present derivations and descriptions of the algorithms in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied and outline prospects for future applications.

Continuous-time Monte Carlo methods for quantum impurity models

We propose a cellular version of dynamical mean field theory which gives a natural generalization of its original single-site construction and is formulated in different sets of variables. We incorporate a possible nonorthogonality of the tight-binding basis set and prove that the resulting equations lead to manifestly causal self-energies.

/pdf/cellular-dynamical-mean-field-approach-to-strongly-4aubhh1r9p.pdf

Cellular Dynamical Mean Field Approach to Strongly Correlated Systems

Correlation effects are important for making predictions in the {delta} phase of Pu. Using a realistic treatment of the intra-atomic Coulomb correlations we address the long-standing problem of computing ground state properties. The equilibrium volume is obtained in good agreement with experiment when taking into account Hubbard U of the order 4 eV. For this U, the calculation predicts a 5f{sup 5} atomiclike configuration with L=5 , S=5/2 , and J=5/2 and shows a nearly complete compensation between spin and orbital magnetic moments. (c) 2000 The American Physical Society.

Ground state theory of delta-Pu

We calculate magnetic anisotropy energy of Fe and Ni by taking into account the effects of strong electronic correlations, spin-orbit coupling, and noncollinearity of intra-atomic magnetization. The LDA+U method is used and its equivalence to dynamical mean-field theory in the static limit is emphasized. Both experimental magnitude of magnetic anisotropy energy and direction of magnetization are predicted correctly near U = 1.9 eV, J = 1.2 eV for Ni and U = 1.2 eV, J = 0.8 eV for Fe. Correlations modify the one-electron spectra which are now in better agreement with experiments.

/pdf/importance-of-correlation-effects-on-magnetic-anisotropy-in-24zizkh335.pdf

Importance of correlation effects on magnetic anisotropy in Fe and Ni

Using a novel approach to calculate optical properties of strongly correlated systems, we address the old question of the physical origin of the alpha--> gamma transition in Ce. We find that the Kondo collapse model, involving both the f and the spd electrons, describes the optical data better than a Mott transition picture involving the f electrons only. Our results compare well with existing experiments on thin films. We predict the full temperature dependence of the optical spectra and find the development of a hybridization pseudogap in the vicinity of the alpha--> gamma phase transition.

/pdf/the-a-g-transition-in-ce-a-theoretical-view-from-optical-2qumuha6qd.pdf

The α → γ Transition in Ce: A Theoretical View from Optical Spectroscopy

Motivated by the recent discovery of superconductivity in infinite-layer $(\text{Sr},\mathrm{Nd}){\mathrm{NiO}}_{2}$ films with Sr content $x\ensuremath{\simeq}0.2$ [D. Li et al., Nature (London) 572, 624 (2019)], we examine the effects of electron correlations and Sr doping on the electronic structure, Fermi-surface topology, and magnetic correlations in $(\text{Nd},\mathrm{Sr}){\mathrm{NiO}}_{2}$ using a combination of dynamical mean-field theory of correlated electrons and band-structure methods. Our results reveal a remarkable orbital-selective renormalization of the Ni $3d$ bands, with ${m}^{*}/m\ensuremath{\sim}3$ and 1.3 for the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals, respectively, that suggests orbital-dependent localization of the Ni $3d$ states. We find that upon hole doping, $(\text{Nd},\mathrm{Sr}){\mathrm{NiO}}_{2}$ undergoes a Lifshitz transition of the Fermi surface which is accompanied by a change of magnetic correlations from three-dimensional (3D) N\'eel $G$-type (111) to quasi-2D $C$-type (110). We show that magnetic interactions in $(\text{Nd},\mathrm{Sr}){\mathrm{NiO}}_{2}$ demonstrate an unanticipated frustration, which suppresses magnetic order, implying the importance of in-plane spin fluctuations to explain its superconductivity. Our results suggest that frustration is maximal for Sr doping $x\ensuremath{\simeq}0.1--0.2$, which is in agreement with an experimentally observed doping value Sr $x\ensuremath{\simeq}0.2$ of superconducting $(\text{Nd},\mathrm{Sr}){\mathrm{NiO}}_{2}$.

S. Y. Savrasov

Papers

Cellular Dynamical Mean Field Approach to Strongly Correlated Systems

Ground state theory of delta-Pu

Importance of correlation effects on magnetic anisotropy in Fe and Ni

The α → γ Transition in Ce: A Theoretical View from Optical Spectroscopy

Lifshitz transition and frustration of magnetic moments in infinite-layer NdNiO 2 upon hole doping