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arXiv:0912.1118

Spectrum of extended systems from Reduced Density Matrix Functional Theory

Sangeeta Sharma, Sam Shallcross, J. K. Dewhurst, Eberhard K. U. Gross

Published Dec 6, 2009• 3 citations
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Abstract

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 $t_{2g}$ and oxygen-$p$ 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.

DOI
10.48550/arxiv.0912.1118

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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.
We demonstrate that reduced density matrix functional theory (RDMFT), in conjunction with the power functional, can successfully treat the nonmagnetic insulating state of the transition metal oxides NiO and MnO, finding for both a gapped single particle spectrum. While long-range spin order is thus not necessary for qualitative agreement with experiment, we find that it is required for good agreement with the X-ray photoemission spectroscopy and Bremsstrahlung isochromat spectroscopy data. We further examine the nature of the natural orbitals in the materials, finding that they display significant Hubbard localization and are, as a consequence, very far from the corresponding Kohn-Sham orbitals. This contrasts with the case of the band insulator Si, in which the Kohn-Sham orbitals are found to be very close to the RDMFT natural orbitals.
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.
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.
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Reduced density matrix functional theory for the case of solids is presented and an exchange-correlation functional based on a fractional power of the density matrix is introduced. We show that compared to other functionals, this produces more accurate behavior for total energies as a function of particle number for finite systems. Moreover, it captures the correct band-gap behavior for conventional semiconductors, as well as strongly correlated Mott insulators, where a gap is obtained in the absence of any magnetic ordering.
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