Optical spectrum of a Hubbard chain

Abstract

The optical absorption of the one-dimensional Hubbard model is calculated by three different methods. Linear chains of five atoms and rings of five and seven atoms containing four electrons are treated numerically. The infinite-chain problem is solved first in the $t$-matrix approximation of Lyo and Holstein. It is shown that in this approximation, most of the high-frequency absorption is due to a bound state which lies above the band continuum. Finally, the absorption is evaluated in the memory-function formalism of G\"otze and W\"olfle, which reduces to ordinary perturbation theory at high frequency. The three approaches are in qualitative agreement, and the differences between them can be explained by the nature of the approximations involved. Applications to tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) and the platinum salt ${\mathrm{K}}_{2}$Pt${(\mathrm{CN})}_{4}$${\mathrm{Br}}_{0.3}$ \ifmmode\cdot\else\textperiodcentered\fi{} 3${\mathrm{H}}_{2}$O (KCP) are discussed.