Minimal model to describe the magnetism of CuGeO3

We show that to describe properly the low-energy excitations of CuGeO3 one must include the effects of a transverse antiferromagnetic coupling, which is estimated to be J(perpendicular to)=0.15J. Owing to this coupling the fr ustration in the chains is significantly lower than recent one-dimensional (1D) estimates based on purely one-dimensional arguments, we find J(2)=0.2J Furthermore, we have found a strong modulation of the nearest-neighbor cou pling due to the static distortion delta=0.065, which is five times higher than that previously deduced from a 1D chain approach. Our set of parameter s gives (i) a value of the distortion which agrees well with some recent es timate for a lower bound we are able to perfectly reproduce, (ii) the dispe rsions, and (iii) the experimental susceptibility at both high and low temp eratures. By performing density matrix renormalization-group (DMRG) calcula tions for two coupled chains we have analyzed the effect of the transverse coupling on the ratio of singlet to triplet gaps. The ratio is very sensiti ve to the parameters and the universality reported in the strict one-dimens ional case is lost. As an additional point, we provide a simple picture to explain the interesting feature observed in recent inelastic neutron-scatte ring experiments: the existence of a second branch of excitations. [S0163-1 829(99)05445-4].