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arXiv:cond-mat/0206203 · Physical Review B

Comment on “Dynamic correlations of the spinless Coulomb Luttinger liquid”

D. W. Wang, Andrew J. Millis, S. Das Sarma

Published Apr 23, 2004• 1 citation
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Abstract

We show that claims [Y. Gindikin and V. A. Sablikov, Phys. Rev. B 65, 125109 (2002)], concerning the threshold behavior of the spectral function of a Coulomb Luttinger liquid, are based on an inconsistent mathematical analysis. Physical arguments are also presented, indicating that the claimed behavior is unlikely to be correct.
DOI
10.1103/physrevb.69.167101

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Received 21 October 2004DOI:https://doi.org/10.1103/PhysRevB.70.159904©2004 American Physical Society

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The dynamic density response function, structure factor, and spectral function of a Luttinger liquid with Coulomb interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The coordinate dependence of the density response is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic structure factor contains the $\ensuremath{\delta}$ peak in the long-wave region, corresponding to one-boson excitations. In addition, the multi-boson-excitations band exists in the wave-number region near to 2kF,{2k}_{F},2kF​, where kF{k}_{F}kF​ is the Fermi wave number. We develop a method to analyze the asymptotic behavior of the spectral functions near to the edges of the multi-boson-excitations band at zero temperature. The dynamic structure factor diverges at the edges of this band, while the dielectric function goes to zero there. Hence, a new collective charge mode appears in the one-dimensional electron liquid as a consequence of short-range dynamic correlations. The mode energy goes to zero at 2kF,{2k}_{F},2kF​, which means that the 2kF{2k}_{F}2kF​ mode is soft.
In the recent preprints the authors claim that conclusions on the violation of the Luttinger sum rule (LSR) as put forward in published papers by the present authors are false or at least not conclusive enough. It concerns the validity of the LSR within the Mott-Hubbard insulator as manifested in the 1D model of spinless fermions, and the Hubbard model on a triangular lattice. We show below that arguments against the presented analysis are rather easily rejected while still the general question of the validity and breakdown of the LSR remains to be answered.
Accurate expressions, valid in experimentally relevant regimes, are presented for the effect of a long-ranged Coulomb interaction on the low-energy properties (momentum distribution function, density of states, electron spectral function, and 4kF{4k}_{F}4kF​ correlation function) of one-dimensional electron systems. The importance of plasmon dispersion (as opposed to exponent) effects in the spectral function is demonstrated.
In a series of papers we combined the Bethe ansatz with a kinetic (Boltzmann) equation in order to compute exactly transport properties in a Luttinger liquid with an impurity. In a recent comment [cond-mat/9708163], Skorik claimed that while our results were correct in linear response, there was a ``serious flaw'' in our calculation at finite voltage. We explain here why Skorik's arguments are inappropriate, and that there is no flaw in our work [cond-mat/9408068; cond-mat/9505031; cond-mat/9503172].