Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

Sofian Teber

doi:10.1140/epjb/e2006-00286-6

paper

Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

arXiv:cond-mat/0511257 · doi:10.1140/epjb/e2006-00286-6

Abstract

We consider one-dimensional (1D) interacting spinless fermions with a non-linear spectrum in a clean quantum wire (non-linear bosonization). We compute diagrammatically the 1D dynamical structure factor, $S(\om,q)$, beyond the Tomonaga approximation focusing on it's tails, $|\om| \gg vq$, {\it i.e.} the 2-pair excitation continuum due to forward scattering. Our methodology reveals three classes of diagrams: two "chiral" classes which bring divergent contributions in the limits $\om \to \pm vq$, {\it i.e.} near the single-pair excitation continuum, and a "mixed" class (so-called Aslamasov-Larkin or Altshuler-Shklovskii type diagrams) which is crucial for the f-sum rule to be satisfied. We relate our approach to the T=0 ones present in the literature. We also consider the $T \neq = 0$ case and show that the 2-pair excitation continuum dominates the single-pair one in the range: $|q|T/k_F \ll \om \mp vq \ll T$ (substantial for $q ≪ k_{F}$ ). As applications we first derive the small-momentum optical conductivity due to forward scattering: $σ\sim 1/\om$ for $T \ll \om$ and $σ\sim T/\om^2$ for $T \gg \om$. Next, within the $2 -$ pair excitation continuum, we show that the attenuation rate of a coherent mode of dispersion $Ω_{q}$ crosses over from $γ_{q} \propto Ω_{q} (q / k_{F})^{2}$ , {\it e.g.} $γ_{q} \sim ∣ q ∣^{3}$ for an acoustic mode, to $γ_{q} \propto T (q / k_{F})^{2}$ , independent of $Ω_{q}$ , as temperature increases. Finally, we show that the $2 -$ pair excitation continuum yields subleading curvature corrections to the electron-electron scattering rate: $τ^{-1} \propto V^2 T + V^4 T^3/\eps_F^2$, where $V$ is the dimensionless strength of the interaction.

arXiv comment(v4) Published version. Details of calculations given (/ referee's comments). No change in previous results. 13 pages, 4 figures. (v3) Extended version (/ referee's comments and recent literature). No change in previous results. 8 pages, 4 figures. (v2) 4 pages, 4 figures. Submitted version (rapid note in EPJB). Kinetic arguments reduced to a footnote. 2 references added

Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

Abstract

References in corpus (7)

Cited by in corpus (16)