Berlin 2008 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 24: Correlated Electrons: Low-dimensional Systems - Models
TT 24.4: Vortrag
Mittwoch, 27. Februar 2008, 14:45–15:00, H 2053
Dynamic structure factor of Luttinger liquids — •Peyman Pirooznia1, Florian Schütz2, and Peter Kopietz1 — 1Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt, Germany — 2Department of Physics, Brown University, Providence, RI 02912, USA
We calculate the dynamic structure factor S ( ω , q ) of non-relativistic fermions with quadratic energy dispersion and long-range density-density interaction, assuming that the Fourier transform fq is the interaction is dominated by momentum transfers q qc ≪ kF, where kF is the Fermi momentum. Using functional bosonization and the known properties of symmetrized closed fermion loops, we obtain an expansion of the inverse irreducible polarization Π∗−1 ( q , ω ) to second order in the small parameter qc / kF . In contrast to conventional bosonization and to direct fermionic perturbation theory, in our approach we do not generate unphysical mass-shell singularities. We then show that for q ≪ qc the width wq of the single-pair particle-hole continuum on the frequency axis scales as q2/m. However, for q → 0 most of the spectral weight is carried by the collective zero sound (ZS) mode, whose damping γq is parametrically smaller than wq. For sharp cutoff in momentum space, fq = f0 Θ ( qc − q ), we find to order ( qc / kF)2 that the ZS mode is not damped at all. For smooth cutoff the ZS damping scales as qn with n ≥ 3 for q → 0, where the value of n depends on the functional form of fq. We also comment on previous attempts to calculate the damping γq of the ZS peak in Luttinger liquids.