Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions

Abstract

We calculate the dynamic structure factor S (omega, q) of spinless fermions in one dimension with quadratic energy dispersion k^2/2m and long range density-density interaction whose Fourier transform f_q is dominated by small momentum-transfers q << q_0 << k_F. Here q_0 is a momentum-transfer cutoff and k_F 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 to second order in the small parameter q_0 / k_F. In contrast to perturbation theory based on conventional bosonization, our functional bosonization approach is not plagued by mass-shell singularities. For interactions which can be expanded as f_q = f_0 + f_0^{2} q^2/2 + O (q^4) with finite f_0^{2} we show that the momentum scale q_c = 1/ | m f_0^{2} | separates two regimes characterized by a different q-dependence of the width gamma_q of the collective zero sound mode and other features of S (omega, q). For q_c << q << k_F we find that the line-shape in this regime is non-Lorentzian with an overall width gamma_q of order q^3/(m q_c) and a threshold singularity at the lower edge.

33 Revtex pages, 17 figures

References in corpus (8)

• Dynamic response of one-dimensional interacting fermions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Coulomb drag by small momentum transfer between quantum wires
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Threshold singularities in the dynamic response of gapless integrable models
• Dynamic structure factor of the Calogero-Sutherland model
• RPAE versus RPA for the Tomonaga model with quadratic energy dispersion

Cited by in corpus (5)

• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature
• Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals
• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem