Triplet dispersion in ${\mathrm{CuGeO}}_3:$ Perturbative analysis

We reconsider the two-dimensional model for ${\mathrm{CuGeO}}_3$ introduced previously [Phys. Rev. Lett. 79, 163 (1997)]. Using a computer aided perturbation method based on flow equations we expand the 1-triplet dispersion up to 10th order. The expansion is provided as a polynom in the model parameters. The latter are fixed by fitting the theoretical result to experimental data obtained by inelastic neutron scattering. For a dimerization $\delta \approx 0.08\left(1\right)\mathrm{}$ we find an excellent agreement with experiment. This value is at least 2 to 3 times higher than values deduced previously from one-dimensional chain approaches. For the intrachain frustration ${\alpha }_0$ we find a smaller value of $0.25\left(3\right).$ The existence of interchain frustration conjectured previously is confirmed by the analysis of temperature-dependent susceptibility.