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arXiv:cond-mat/0003464 · Journal of the Physical Society of Japan

Role of Phase Variables in Quarter-Filled Spin Density Wave States

Yuh Tomio, Yoshikazu Suzumura

Published Mar 15, 2000• 25 citations
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Abstract

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, $θ$ and $ϕ$, where $θ$ expresses the charge fluctuation of SDW and $ϕ$ 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 $θ$ and/or $ϕ$ disappears for the interactions, which lead to the boundary between the pure 2k_F-SDW state and the corresponding coexistent state.

DOI
10.1143/jpsj.69.796

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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.
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.
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 reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.
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.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.
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.