Luttinger parameters and momentum distribution function for the half-filled spinless fermion Holstein model: A DMRG approachS. Ejima and H. Fehske
Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald - 17489 Greifswald, Germany, EU
received 8 May 2009; accepted in final form 6 July 2009; published July 2009
published online 22 July 2009
We reexamine the nature of the metallic phase of the one-dimensional half-filled Holstein model of spinless fermions. To this end, we determine the Tomonaga-Luttinger–liquid correlation parameter by large-scale density matrix renormalisation group (DMRG) calculations, exploiting i) the leading-order scaling relations between the ground-state energy and the single-particle excitation gap and ii) the static charge structure factor in the long-wavelength limit. While both approaches give almost identical results for intermediate-to-large phonon frequencies, we find contrasting behaviour in the adiabatic regime: i) > 1 (attractive) vs. ii) < 1 (repulsive). The latter result for the correlation exponent is corroborated by data obtained for the momentum distribution function n(k), which puts the existence of an attractive metallic state in the spinless fermion Holstein model into question. We conclude that the scaling relation must be modified in the presence of electron-phonon interactions with noticeable retardation.
71.10.Hf - Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems.
71.38.-k - Polarons and electron-phonon interactions.
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