We calculate the optical conductivity of LiV$_{ 2}$O$_{ 5}$ and NaV$_{ 2}$O$_{ 5}$ using exact numerical diagonalization of a quarter-filled extended Hubbard model on a system of coupled ladders. In particular, electronic correlations are treated exactly, and a quantitative agreement between calculated and experimentally observed optical conductivity of these two vanadium oxides is presented. Furthermore, it is found that LiV$_{ 2}$O$_{ 5}$ differs from NaV$_{ 2}$O$_{ 5}$ not only in the charge ordering pattern but also in the nature of the inter-ladder coupling: In contrast to LiV$_{ 2}$O$_{ 5}$, in NaV$_{ 2}$O$_{ 5}$ neighboring ladders are coupled by a strong Coulomb repulsion, and not by inter-ladder hopping.
Categories: cond-mat.str-el