Recent theoretical developments to better understand strongly bound local Frenkel excitons in “charge-transfer insulators” will be presented. First, the description of charge-transfer insulators will be unified with that of the Mott insulators via the use of symmetry-respecting first-principles Wannier functions. Second, formal theoretical framework of TD-DFT with LDA+U will be developed and applied to a case study illustrating its capability and deficiency. Third, systematic framework of strong coupling approach will be presented to account for the multiplets beyond the typical first-principles approximations. Finally, a two-particle hopping kernel is introduced to describe propagation of the local excitations. Case studies include anisotropy of local excitations in NiO , missing neutron spectral weight of the cuprates , and space-time propagation of excitons in LiF .
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 P. Abbamonte et al, Proc. Natl. Acad. Sci. 105, 12159 (2008).
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