Damping of zero sound in Luttinger liquids
Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany
Corresponding author: a email@example.com
Revised: 30 July 2007
Published online: 8 September 2007
We calculate the damping γq of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k2 / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γq from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /kF ≪F (where kF = m vF is the Fermi wave-vector) we find to leading order γq ∝| q |3 /(vF m2). On the other hand, for F ≪| q| /kF most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q2/m. We also show that zero sound damping leads to a finite maximum proportional to |k - kF | -2 + 2 η of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K0.3MoO3. We comment on other recent calculations of γq.
PACS: 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 71.10.-w – Theories and models of many-electron systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007