Fourier transform of the $2k_F$ Luttinger liquid density correlation function with different spin and charge velocities

Abstract

We obtain a closed-form analytical expression for the zero temperature Fourier transform of the $2k_F$ component of the density-density correlation function in a Luttinger liquid with different spin and charge velocities. For frequencies near the spin and charge singularities approximate analytical forms are given and compared with the exact result. We find power law like singularities leading to either divergence or cusps, depending on the values of the Luttinger parameters and compute the corresponding exponents. Exact integral expressions and numerical results are given for the finite temperature case as well. We show in particular how the temperature rounds the singularities in the correlation function.

8 pages, 3 figures. Minor changes, updated references

References in corpus (4)

• Spin-charge separation and localization in one-dimension
• Coulomb drag by small momentum transfer between quantum wires
• Green's function for magnetically incoherent interacting electrons in one dimension
• Non-equilibrium charge noise and dephasing from a spin-incoherent Luttinger liquid

Cited by in corpus (5)

• Spin-charge separation in two-component Bose-gases
• Collective excitations in one-dimensional ultracold Fermi gases: a comparative study
• Quantum interference and spin-charge separation in a disordered Luttinger liquid
• Signatures of Strong Correlations in One-Dimensional Ultra-Cold Atomic Fermi Gases
• Junctions of Spin-Incoherent Luttinger Liquids with Ferromagnets and Superconductors