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arXiv:cond-mat/0009238 · Physical review. B, Condensed matter

One-dimensional spinless fermion model with competing interactions beyond half filling

A. K. Zhuravlev, Mikhail I. Katsnelson

Published Jun 18, 2001• 20 citations
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Abstract

An accurate numerical consideration of one-dimensional (1D) spinless fermion model with next-nearest-neighbor interactions is carried out for the electron concentration \ensuremath{\rho}=4/7. It is shown that depending on the parameters of the model, it can be either Luttinger liquid or bipolaron liquid. In the former case, competing interactions can result in a smooth behavior of one-electron distribution function at the Fermi surface with a divergence in the second derivative with respect to the quasimomentum (and not in the first one, as usual). In this connection, uncommon photoemission spectra for some 1D conductors can be explained qualitatively.

DOI
10.1103/physrevb.64.033102

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An accurate numerical consideration of one-dimensional (1D) spinless fermion model with next-nearest-neighbor interactions is carried out for the electron concentration \ensuremath{\rho}=4/7. It is shown that depending on the parameters of the model, it can be either Luttinger liquid or bipolaron liquid. In the former case, competing interactions can result in a smooth behavior of one-electron distribution function at the Fermi surface with a divergence in the second derivative with respect to the quasimomentum (and not in the first one, as usual). In this connection, uncommon photoemission spectra for some 1D conductors can be explained qualitatively.
The Haldane hypothesis about the universality of the Luttinger liquid (LL) behavior in conducting one-dimensional fermion systems is checked numerically for the spinless fermion model with next-nearest-neighbor interactions. It is shown that for the large enough interactions the ground state can be gapless due to frustrations but at the same time might not belong to the same universality class as a simple LL. The exponents of the correlation functions for this unusual conducting state are found numerically by a finite-size method.
We consider the spinless fermion model with hard-core repulsive potential between particles extended on a few lattice sites δ. The Luttinger-liquid behavior is studied for different values of a hard-core radius. We derive a critical exponent Θ of the one-particle correlation function ⟨ c i † c j ⟩ for an arbitrary electron density and coupling constant. Our results show that at high density the behavior of fermions can be described as a strongly interacting Luttinger liquid with Θ > 1. As a result, the residual Fermi surface disappears.
We consider the spinless fermion model with hard-core repulsive potential between particles extended on a few lattice sites delta. The Luttinger-liquid behavior is studied for different values of a hard-core radius. We derive a critical exponent Theta of the one-particle correlation function [c(i)(dagger)c(j)] for an arbitrary electron density and coupling constant. Our results show that at high density the behavior of fermions can be described as a strongly interacting Luttinger liquid with Phi > 1. As a result, the residual Fermi surface disappears.
One parametric one-dimensional spinless fermion model is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many-particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interaction. The ground-state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.
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.
One parametric one-dimensional spinless fermion models is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interactions. The ground state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.