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

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dc.creatorPirooznia, Peyman
dc.creatorSchuetz, Florian
dc.creatorKopietz, Peter
dc.date2008-02-07
dc.date.accessioned2026-07-07T09:56:35Z
dc.date.available2026-07-07T09:56:35Z
dc.descriptionWe 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.
dc.description33 Revtex pages, 17 figures
dc.identifierhttps://arxiv.org/abs/0802.0970
dc.identifierhttp://arxiv.org/abs/0802.0970
dc.identifierPhys. Rev. B 78, 075111 (2008)
dc.identifierdoi:10.1103/PhysRevB.78.075111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167027
dc.subjectStrongly Correlated Electrons
dc.subjectStatistical Mechanics
dc.titleDynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions
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