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We obtain a closed-form analytical expression for the zero temperatureFourier transform of the $2k_F$ component of the density-density correlationfunction in a Luttinger liquid with different spin and charge velocities. Forfrequencies near the spin and charge singularities approximate analytical formsare given and compared with the exact result. We find power law likesingularities leading to either divergence or cusps, depending on the values ofthe Luttinger parameters and compute the corresponding exponents. Exactintegral expressions and numerical results are given for the finite temperaturecase as well. We show in particular how the temperature rounds thesingularities in the correlation function.Comment: 8 pages, 3 figures. Minor changes, updated reference

physical review b

Fourier transform of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mi>F</mml:mi></mml:msub></mml:mrow></mml:math>Luttinger liquid density correlation function with different spin and charge velocities

Fourier transform of the2kFLuttinger liquid density correlation function with different spin and charge velocities