2005/11/30 by S. Teber, Sofian Teber · 3 citations
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Atomic and Subatomic Physics Research #Crystallography and Radiation Phenomena #cond-mat.str-el
paper · pdf · doi:10.1140/epjb/e2006-00286-6
published as Eur. Phys. J. B 52, 233 (2006) · (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
openalex publication_date 2006/07/01 · arxiv created 2006/09/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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| ≫ 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 → ± 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\not=0 case and show that the 2-pair excitation continuum dominates the single-pair one in the range: |q|T/kF ≪ \om ∓ vq ≪ T (substantial for q ≪ kF). As applications we first derive the small-momentum optical conductivity due to forward scattering: σ∼ 1/\om for T ≪ \om and σ∼ T/\om2 for T ≫ \om. Next, within the 2-pair excitation continuum, we show that the attenuation rate of a coherent mode of dispersion Ωq crosses over from γq ∝ Ωq (q/kF)2, \it e.g. γq ∼ |q|3 for an acoustic mode, to γq ∝ T (q/kF)2, independent of Ωq, as temperature increases. Finally, we show that the 2-pair excitation continuum yields subleading curvature corrections to the electron-electron scattering rate: τ-1 ∝ V2 T + V4 T3/\epsF2, where V is the dimensionless strength of the interaction.