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arXiv:1607.08410 · Physical review. B./Physical review. B

Photoemission spectra from reduced density matrices: The band gap in strongly correlated systems

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

Published Oct 25, 2016• 30 citations
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Abstract

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 $G$, whose imaginary part is related to photoemission spectra, and we introduce a frequency-dependent effective energy that accounts for all the poles of $G$. 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.

DOI
10.1103/physrevb.94.155141

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Physical review. B, Condensed matter•Dec 15, 1994•158 citations
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.
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 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.
Abstract Strongly correlated systems pose a challenge for theoretical methods based on an independent electron approximation. Such methods struggle to predict a nonzero gap in Mott insulators or to capture the correct physics of the insulator-to-metal phase transition in strongly correlated materials. In a recent paper by Shinohara et al (2015 New J. Phys. 17 093038 ) it is shown that strongly correlated materials and correct descriptions of their phase transitions are within the reach of reduced density matrix functional theory (RDMFT) approximations. For a doping-induced phase transition, not only is a satisfactory agreement with experimental spectra found for NiO but it is also shown that the physical picture of the observed Mott transition stays in line with more computationally demanding many-body theories. This is an important step toward providing an RDMFT–based computation tool for studying strongly correlated materials.
We present an original approach for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the GWGWGW method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. Our method uses as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts. We show that, contrary to the one-body Green's function, satellites are already present in the corresponding non-interacting Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We also show how the one-body Green's function can be retrieved from the three-body Green's function. We illustrate our approach by applying it to the symmetric Hubbard dimer.
We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the GWGWGW method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. To this end we use as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts, and we show how the one-body Green's function, and hence the corresponding spectral function, can be retrieved from it. We show that, contrary to the one-body Green's function, information about satellites is already present in the non-interacting three-body Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We give a proof of principle of our strategy by applying it to the Hubbard dimer, for which the exact self-energy is available.
Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-Tc{\mathit{T}}_{\mathit{c}}Tc​) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.