Damping of zero sound in Luttinger liquids

TL;DR

This paper calculates the damping of zero sound in a one-dimensional Fermi gas with interactions, revealing a cubic dependence on wave-vector and matching experimental photoemission data for blue bronze.

Contribution

It provides a theoretical calculation of zero-sound damping in Luttinger liquids with quadratic dispersion, including the dependence on interaction strength and comparison with experimental results.

Findings

Gamma_q scales as |q|^3 for small q.

Zero-sound damping causes a finite maximum in the spectral function.

Predictions agree with photoemission data for K_{0.3}MoO_3.

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.