Reduced density-matrix functional theory: Correlation and spectroscopy

Abstract

In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard molecule at 1/4 and 1/2 filling as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis are made concerning the approximations of the observables. In particular we focus on the atomic limit, where the two sites of the molecule are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard molecule at 1/2 filling with or without a spin-symmetry-broken ground state, allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW the signature of strong correlation are present in the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover we show how the spectroscopic properties change from one spin structure to the other. Our findings can be generalized to other situations, which allows us to make connections to real materials and experiment.

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

“…This is in line with an analogous analysis on the Hubbard dimer. 38 It still remains to improve the band gap, which is overestimated in our method. This finding is consistent with the results on large Hubbard rings, which indicate that this overestimation is due to the use of δ (1) , and that the use of δ (2) might improve the spectrum and the band gap.…”

“…We obtain good results (although the power functional does not recover the particle-hole symmetry) and, in particular, the band gap opens in the atomic limit, without breaking the symmetry. 38 We note that the gap strongly depends on the value of α: it has its maximum value for α = 0.5 while it disappears for α = 1 which corresponds to HF. For comparison we also report the results obtained using GW and the DER method: in the atomic limit these methods do not open any gap, unless the symmetry of the system is broken.…”

Reduced density-matrix functionals from many-particle theory

“…j , which gives the exact groundstate energy for the half-filled Hubbard dimer [18,54]. We have however shown that the Müller functional predicts an unphysical infinite magnetic susceptibility for the half-filled Hubbard dimer [19].…”

“…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.…”

“…We describe the DFT+RDMFT scheme and new approaches to approximate the density-matrix functional. New functionals are necessary, because despite the success of simple functionals within RDMFT, the most common density-matrix functionals reproduce a number of features in a qualitatively incorrect manner [17][18][19]]. …”