Damping of zero sound in Luttinger liquids
arXiv:cond-mat/0512494 · doi:10.1140/epjb/e2007-00235-y
Abstract
We calculate the damping gamma_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k^2 / 2 m at zero temperature. For wave-vectors | q| /k_F small compared with F we find to leading order gamma_q = v_F^{-1} m^{-2} Y (F) | q |^3, where v_F is the Fermi velocity, k_F is the Fermi wave-vector, and Y (F) is proportional to F^3 for small F. We also show that zero-sound damping leads to a finite maximum proportional to |k - k_F |^{-2 + 2 eta} of the charge peak in the single-particle spectral function, where eta is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_{0.3}MoO_3.
final version as published; with more technical details; we have added a discussion of recent work which appeared after our initial cond-mat posting; 13 pages, 5 figures
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Cited by in corpus (8)
- One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
- Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
- Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions
- Parametric resonance and spin-charge separation in 1D fermionic systems
- One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
- Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics
- One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem
- Investigating the roots of the nonlinear Luttinger liquid phenomenology