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arXiv:cond-mat/0004007

A Pseudogap in the Single-Particle Density of States of a Tomonaga-Luttinger Liquid

Emiliano Papa, Alexei M. Tsvelik

Published Apr 2, 2000• 0 citations
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Abstract

We study a single-particle density of states (DOS) in a model of Tomonaga-Luttinger liquid with small (large) values of the Luttinger parameter $K_\rc < 0.17$, ($K_\rc > 5.82$), in the charge sector. We explain that such values of $K_\rc$ may be achieved by electron-phonon interactions without generating the spin gap. We suggest that electron-phonon interactions can be partially incorporated into the Tomonaga-Luttinger liquid scheme by introducing frequency dependent $K_\rc(ω)$. We demonstrate that when the low-frequency asymptotic value $K_\rc(0) < 0.17$ or $K_\rc(0) > 5.82$, the single-particle DOS has a pseudogap behavior in frequency where $ρ(ω)/ω$ vanishes at small frequencies. The DOS exhibits a peak the position of which scales as $[K(0) + K^{-1}(0)]ω_0/2$ where $ω_0$ is the characteristic phonon frequency.

DOI
10.48550/arxiv.cond-mat/0004007

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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 K ρ 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) K ρ >1 (attractive) vs. ii) K ρ < 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.
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