Spin Dynamics of the One-DimensionalJ-J' Model and Spin-Peierls Transition in CuGeO₃

Abstract

Spin dynamics as well as static properties of the one-dimensional J-J ′ model (S = 1/2, J > 0 and 0 ≤ α = J ′ /J ≤ 0.5) are studied by the exact diagonalization and the recursion method of finite systems up to 26 sites. Especially, the dynamical structure factor S(q, ω) is investigated carefully for various values of α. As α increases beyond the gapless-gapful critical value αc = 0.2411, there appear features definitely different from the Heisenberg model but the same with the Majumdar-Ghosh model. Some of these features depend only on the value of α and not on δ: a parameter introduced for the coupling alternation. By comparing these results with a recent inelastic neutron scattering spectrum of an inorganic spin-Peierls compound CuGeO3 [M. Arai et al. : Phys. Rev. Lett. 77 (1996) 3649], it is found that the frustration by J ′ in CuGeO3 is unexpectedly strong (α = 0.4-0.45), and at least α must be larger than αc to some extent. The value of J is evaluated at ∼ 180K consistent with other estimations. The coupling alternation is extremely small. This large frustration is a primary origin of the various anomalous properties CuGeO3 possesses. For comparison we refer also to α ′ -NaV2O5.

Dynamical structure factors ofS=1bond-alternating Heisenberg chains

“…The size dependence of the residues in both regions of wave numbers is quite similar to that for the excitation continua of the S = 1/2 [30] and 1 [9] isotropic Heisenberg chains. The behavior of the residue around q = 0.9π at α = 0.7 is different from that in the other wave numbers.…”

“…Note that the finite-size effects only for the residues are presented, since the positions of the poles scarcely depend on the system size. We discuss the results, making reference to the typical size dependence of the excitation continua for the S = 1/2 [30] and 1 [9] isotropic Heisenberg chains.…”

“…To discuss whether the lowest excited states in given q form an isolated mode or a lower edge of the excitation continuum in the thermodynamic limit, we investigate the finite-size effects of the poles and their residues of the continued fraction C z (q, ω) [9,30]. As reported in Refs.…”

Spin Excitation and Phonon Effect for Frustrated Spin-Peierls Model

“…The differences are consistent with the previous studies on the spin DSF. 2,22) The spin DSF in the dimer phase seems to capture the exper- imental features of CuGeO 3 15) showing large weights around k = π/2 and at the upper edge of the continuum. Note that we cannot see the splitting of the lowest-energy excitations from the continuum, i.e., the bound state of two spinons in the dimer phase.…”

“…On the contrary, recent studies have shown that the spinPeierls state is not stable at zero temperature with phonons in the antiadiabatic limit. [1][2][3][4] At the same time, these studies have shown that there is a critical coupling of the transition between these states. Namely, for the coupling constant α < α c , the ground state is the spin-liquid state, but for α > α c , it is the spin-Peierls state.…”