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arXiv:cond-mat/0101450 · Physical review. B, Condensed matter

Effect of nearest- and next-nearest neighbor interactions on the spin-wave velocity of one-dimensional quarter-filled spin-density-wave conductors

Yuh Tomio, N. Dupuis, Yoshikazu Suzumura

Published Sep 11, 2001• 10 citations
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Abstract

We study spin fluctuations in quarter-filled one-dimensional spin-density-wave systems in presence of short-range Coulomb interactions. By applying a path integral method, the spin-wave velocity is calculated as a function of on-site $(U),$ nearest (V) and next-nearest ${(V}_{2})$ neighbor-site interactions. With increasing V or ${V}_{2},$ the pure spin-density-wave state evolves into a state with coexisting spin- and charge-density waves. The spin-wave velocity is reduced when several density waves coexist in the ground state, and may even vanish at large V. The effect of dimerization along the chain is also considered.

DOI
10.1103/physrevb.64.125123

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We study spin fluctuations in quarter-filled one-dimensional spin-density-wave systems in presence of short-range Coulomb interactions. By applying a path integral method, the spin-wave velocity is calculated as a function of on-site (U),(U),(U), nearest (V) and next-nearest (V2){(V}_{2})(V2​) neighbor-site interactions. With increasing V or V2,{V}_{2},V2​, the pure spin-density-wave state evolves into a state with coexisting spin- and charge-density waves. The spin-wave velocity is reduced when several density waves coexist in the ground state, and may even vanish at large V. The effect of dimerization along the chain is also considered.
Spin-wave excitations of quarter-filled spin-density-wave state, which coexists with charge ordering, have been studied for one-dimensional extended Hubbard model with the nearest-neighbor repulsive interaction (V) and next-nearest-neighbor one (V_2). We calculate dispersion relations for the acoustic and optical spin-wave within the random phase approximation. Our numerical calculation shows that energy spectrum of the acoustic branch is well described by a simple sine function form. In the states coexisting with charge-density-wave, the spin-wave velocity decreases with increasing V or V_2. Our numerical result, that velocity reduces to zero in the limit of large V or V_2, is analyzed in terms of a spin 1/2 Heisenberg model with effective antiferromagnetic exchange interaction.
Several kinds of spin density wave (SDW) states with both quarter-filled band and dimerization are reexamined for a one-dimensional system with on-site, nearest-neighbor and next-nearest-neighbor repulsive interactions, which has been investigated by Kobayashi et al. (J. Phys. Soc. Jpn. 67 (1998) 1098). Within the mean-field theory, the ground state and the response to the density variation are calculated in terms of phase variables, θθθ and ϕϕϕ, where θθθ expresses the charge fluctuation of SDW and ϕϕϕ describes the relative motion between density wave with up spin and that with down spin respectively. It is shown that the exotic state of coexistence of 2k_F-SDW and 2k_F-charge density wave (CDW) is followed by 4k_F-SDW but not by 4k_F-CDW where k_F denotes a Fermi wave vector. The harmonic potential with respect to the variation of θθθ and/or ϕϕϕ disappears for the interactions, which lead to the boundary between the pure 2k_F-SDW state and the corresponding coexistent state.
The collective modes representing density fluctuation in a spin density wave (SDW) have been examined for a one-dimensional electron system of a quarter-filled extended Hubbard model with the next-nearest-neighbor interaction ( V 2 ). Within the random phase approximation (RPA), we obtain a new collective mode, which appears with increasing V 2 . The mode describes the relative motion between density wave with up spin and that with down spin. The gap in the excitation spectrum vanishes at a critical value of V 2 corresponding to the onset of the coexistence of 2 k F -SDW, 2 k F -charge density wave and 4 k F -SDW in the ground state ( k F being the Fermi wave vector).
We examine effects of the next-nearest-neighbor repulsion on electronic states of a one-dimensional interacting electron system which consists of quarter-filled band and interactions of on-site and nearest-neighbor repulsion. We derive the effective Hamiltonian for the electrons around wave number $\pm \kf$ ($\kf$: Fermi wave number) and apply the renormalization group method to the bosonized Hamiltonian. It is shown that the next-nearest-neighbor repulsion makes $4\kf$-charge ordering unstable and suppresses the spin fluctuation. Further the excitation gaps and spin susceptibility are also evaluated.
We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor ttt and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where ttt (>0)(>0)(>0) is much smaller than ${t}^{\ensuremath{'}}$ (>0)(>0)(>0). First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral ttt $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.
A one-dimensional electron system at quarter-filling has been examined by applying the renormalization group method to a bosonized model with on-site (U) and nearest-neighbor (V) repulsive interactions. By evaluating both normal scattering and Umklapp scattering perturbatively, we obtain a phase diagram in which a metallic state with a 2k_F spin density wave (k_F is the Fermi wave number) moves into an insulating state with charge disproportionation of a 4k_F charge density wave with an increase in both U and V. The effect of the next-nearest-neighbor repulsion is also discussed.