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Journal of Chemical Theory and Computation

Many-Body Effective Energy Theory: Photoemission at Strong Correlation

S. Di Sabatino, J. A. Berger, Pina Romaniello

Published Aug 7, 2019• 10 citations
Publisher

Abstract

In this work, we explore the performance of a recently derived many-body effective energy theory for the calculation of photoemission spectra in the regime of strong electron correlation. We apply the theory to paramagnetic MnO, FeO, CoO, and NiO, which are typical examples of strongly correlated materials and, therefore, a challenge for standard theories. We show that our method opens a correlation gap in all of the oxides studied without breaking the symmetry. Although the materials seem similar, we show that an analysis of the occupation numbers reveals that the nature of the gap is not the same for these materials. Overall, the results are very promising, although improvements are clearly required, since the band gap is overestimated for all of the systems studied. We indicate some possible strategies to further develop the theory.

DOI
10.1021/acs.jctc.9b00427

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In this work, we explore the performance of a recently derived many-body effective energy theory for the calculation of photoemission spectra in the regime of strong electron correlation. We apply the theory to paramagnetic MnO, FeO, CoO, and NiO, which are typical examples of strongly correlated materials and, therefore, a challenge for standard theories. We show that our method opens a correlation gap in all of the oxides studied without breaking the symmetry. Although the materials seem similar, we show that an analysis of the occupation numbers reveals that the nature of the gap is not the same for these materials. Overall, the results are very promising, although improvements are clearly required, since the band gap is overestimated for all of the systems studied. We indicate some possible strategies to further develop the theory.
We present a method for the calculation of photoemission spectra in terms of reduced density matrices. We start from the spectral representation of the one-body Green's function GGG, whose imaginary part is related to photoemission spectra, and we introduce a frequency-dependent effective energy that accounts for all the poles of GGG. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong correlation regime. In real systems reduced density matrices can be obtained from reduced density-matrix functional theory. Here we use this approach to calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and paramagnetic phases, contrary to mean-field methods, in which the paramagnet is a metal.
We present a method for calculating the spectrum of extended solids within reduced density matrix functional theory. An application of this method to the strongly correlated transition metal oxide series demonstrates that (i) an insulating state is found in the absence of magnetic order and, in addition, (ii) the interplay between the change transfer and Mott-Hubbard correlation is correctly described. In this respect we find that while NiO has a strong charge transfer character to the electronic gap, with substantial hybridization between t2gt_{2g}t2g​ and oxygen-ppp states in the lower Hubbard band, for MnO this is almost entirely absent. As a validation of our method we also calculate the spectra for a variety of weakly correlated materials, finding good agreement with experiment and other techniques.
A variety of quantum many-body methods have been developed for studying the strongly correlated electron systems. We have also proposed a computationally efficient and accurate approach, named the correlation matrix renormalization (CMR) method to address the challenges. The theoretic development and benchmark tests of the CMR method are included in this thesis. Meanwhile, ground state total energy is the most important property of electronic calculations. We also investigated an alternative approach to calculate the total energy, and extended this method for magnetic anisotropy energy of ferromagnetic materials. In addition, another theoretical tool, dynamical mean-field theory on top of the density functional theory, has also been used in electronic structure calculations for an Iridium oxide to study the phase transition, which results from an interplay of the d electrons' internal degrees of freedom.
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and its compounds including iron-based superconductors and perovskite oxides, as well as organic conductors of kappa-ET type.
The self-energy of a translational invariant system of interacting fermions may be expanded in diagrams contributing to the self-energy of finite clusters with open boundary conditions. The exact solution of small clusters might therefore be used to construct a systematic approximation to the self-energy of the infinite system. This approximation incorporates both the local and the itinerant degrees of freedom on an equal footing. We develop this method for the one-band Hubbard Hamiltonian and apply it to the three-band Hamiltonian of the CuO superconductors. Already the lowest nontrivial approximation yields interesting results for the spectral density useful for the interpretation of photoemission experiments. We find (i) transfer of spectral weight from the upper to the lower Hubbard band upon doping, (ii) the formation of an isolated band of Zhang-Rice singlets separated from the band of triplet states by a many-body gap, and (iii) creation of density of states above the top of the oxygen band upon doping.
Three-body problem involving two valence holes and a single conduction electron, which appears in the study of the final state of the resonant photoemission in insulators and semiconductors, is formulated to be solved exactly in a two-band Hubbard model by use of Faddeev's scattering theory. The wave functions and energy eigenvalues are calculated numerically in a one-dimensional model. By use of this exact solution of the three-body problem, resonance photoemission spectra are studied from a weak correlation resion to a strong one. It is shown that the approximation used in the past analysis, in which two valence holes are assumed to be localized, deviates from the present results even in the strong correlation region U v v ∼2 W v with U v v and W v denoting the Coulomb integral and the band width of valence holes, respectively.