Intraband absorption in a low-density Hubbard chain

Abstract

We have investigated the intraband absorption in a single-band Hubbard model at a low concentration $c$ ($c$ is unity for a filled band) of electrons with a particular emphasis on one-dimensional nearest-neighbor electron transfer. Using a two-particle approximation, we find, for the latter in the frequency range $c\ensuremath{\ll}\ensuremath{\hbar}\ensuremath{\omega}$ (the bandwidth is unity) that the absorption is independent of frequency and vanishes as ${U}^{\ensuremath{-}2}$ for a large on-site Coulomb repulsion $U$. The absorption occurs when an electron is accelerated by another electron in the presence of an oscillating field (i.e., inverse bremsstrahlung). The transport relaxation rate is given by ${\ensuremath{\tau}}^{\ensuremath{-}1}\ensuremath{\propto}c{\ensuremath{\omega}}^{2}{U}^{\ensuremath{-}2}$. In the limit $U=\ensuremath{\infty}$ the present result supports the spinless fermion model, according to which the intraband absorption vanished for $\ensuremath{\omega}\ensuremath{\ne}0$. In the presence of second-nearest-neighbor electron transfer (${t}_{2}$) such that $c\ensuremath{\ll}|{t}_{2}|$, the ${\ensuremath{\omega}}^{\ensuremath{-}2}$-frequency dependence of the absorption obtains as in two or three dimensions.