Journal
PHYSICAL REVIEW B
Volume 75, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.75.205116
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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.
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