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.

arXiv comment33 Revtex pages, 17 figures

References in corpus (24)

• 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
• Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model
• Coulomb drag by small momentum transfer between quantum wires
• Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation
• 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
• Functional Bosonization of Interacting Fermions in Arbitrary Dimensions
• Dynamic structure factor of the Calogero-Sutherland model
• Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking
• Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems
• Luttinger liquids with curvature: Density correlations and Coulomb drag effect
• Bosonization approach to charge and spin dynamics of 1D fermions with band-curvature
• How to bosonize fermions with non-linear energy dispersion
• Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation
• Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy
• Damping of zero sound in Luttinger liquids
• Exact integral equation for the renormalized Fermi surface
• Singularity Cancellation in Fermion Loops through Ward Identities
• Reduction formula for fermion loops and density correlations of the 1D Fermi gas
• Damping of long-wavelength collective excitations in quasi-onedimensional Fermi liquids
• How does a quadratic term in the energy dispersion modify the single-particle Green's function of the Tomonaga-Luttinger model?
• RPAE versus RPA for the Tomonaga model with quadratic energy dispersion

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• 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
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Investigating the roots of the nonlinear Luttinger liquid phenomenology