Abstract
We calculate the one-particle spectral function and the corresponding derived quantitiesfor a chain lattice with a one-dimensional conducting electron band, and with athree-dimensional long-range Coulomb electron–electron interaction treated within theG0W0 approximation. It is shown that due to the anisotropic acoustic dispersion of the plasmonmode, the quasi-particle peak as a standard Fermi liquid feature does not show upin the spectral function. Instead, the latter comprises only a broad maximumwith width of the order of plasmon energy. Such spectral properties are in thequalitative agreement with ARPES spectra of Bechgaard salts obtained in recentmeasurements. The present approach is appropriate for the treatment of wide energy scalesdefined by the width of the conducting band and the plasmon energy, and iscomplementary to earlier rigorous results obtained within the Luttinger liquidapproach in the asymptotic limit of low energies close to the chemical potential.
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