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

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.

Reduced density-matrix functionals from many-particle theory

“…It should be noted here, that the band gap was estimated by an extrapolation technique [67] due to the missing derivative discontinuity. Applications to transition metal oxides investigated the parameter dependence [68,69] as well as metal-insulator transitions [70,71] and showed good agreement with other methods. However due to the antiferromagnetic ground state of the transition metal oxides under investigation, the pathologies of the power functional for the prediction of magnetic structures did not become apparent.…”

“…Properties like spectra or static response functions, like static dipole polarizabilities [102], however are not directly accessible. Several methods have been proposed to estimate photoemission spectra starting from Slater's transition state [70,103], local RDMFT [104,105] and approximations in terms of higher order RDMs [69]. Applications of these approaches to models systems [18,69] as well as real materials [69][70][71] showed mixed performances.…”

Many-Body Effective Energy Theory: Photoemission at Strong Correlation

“…As commented in Ref. [1] the various approximations δ R/A,n i (ω) are related to the first n-th moments µ…”

“…In this section we give the key equations of the manybody effective energy theory derived in Ref. [1] as well as the basic equations of reduced density-matrix functional theory.…”

“…(and similarly for G A ii ). At the level of δ R/A, (1) , the Green's function depends only on the first moment, while neglecting all the higher-order frequency-dependent corrections. As illustrated in Fig.…”