Resistivity of a one-dimensional interacting quantum fluid

Abstract

The frequency and temperature dependence of the conductivity of a one-dimensional fermion system with attractive interactions is studied by using a renormalization-group technique. At half filling the real part of the conductivity has both a δ(ω) part and a divergent frequency behavior ${\mathrm{\omega }}^{\mathrm{-}\nu }$ at finite frequencies, where ν is a nonuniversal exponent depending on the interactoins. For the particular case of the attractive Hubbard model, logarithmic corrections appear and the conductivity behaves as 1/[ω ${\log }_{10}^2$(ω)], plus a δ(ω) part. Away from half filling the conductivity has a δ(ω) part and a gap up to a critical frequency ${\mathrm{\omega }}_{\mathit{c}}$, where ${\mathrm{\omega }}_{\mathit{c}}$ is proportional to the doping with a prefactor depending on the interactions. The results obtained for the fermion model can be straightforwardly extended to the conductivity of an interacting one-dimensional boson model.