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Abstract

A first-principles understanding of the electronic properties of f -electron systems is currently regarded as a
great challenge in condensed-matter physics because of the difficulty in treating both localized and itinerant states
on the same footing by the current theoretical approaches, most notably density-functional theory (DFT) in the
local-density or generalized gradient approximation (LDA/GGA). Lanthanide sesquioxides (Ln2O3) are typical
f -electron systems for which the highly localized f states play an important role in determining their chemical
and physical properties. In this paper, we present a systematic investigation of the performance of many-body
perturbation theory in the GW approach for the electronic structure of the whole Ln2O3 series. To overcome
the major failure of LDA/GGA, the traditional starting point for GW, for f -electron systems, we base our GW
calculations on Hubbard U corrected LDA calculations (LDA+U). The influence of the crystal structure, the
magnetic ordering, and the existence of metastable states on the electronic band structures are studied at both
the LDA+U and the GW level. The evolution of the band structure with increasing number of f electrons is
shown to be the origin for the characteristic structure of the band gap across the lanthanide sesquioxide series. A
comparison is then made to dynamical mean-field theory (DMFT) combined with LDA or hybrid functionals to
elucidate the pros and cons of these different approaches.