Minimal model to describe the magnetism of CuGeO₃

We show that to describe properly the low energy excitations of $CuGeO_{3}$ one must include the effects of a transverse antiferromagnetic coupling, which is estimated to be $J_{\perp}=0.15 J$. Owing to this coupling the frustration in the chains is significantly lower than recent 1D estimates based on purely one-dimensional arguments, we find $J_{2}=0.2 J$. Furthermore we have found a strong modulation of the nearest neighbour coupling due to the static distortion $\delta = 0.065$, which is 5 times higher than that previously deduced from a 1D chain approach. Our set of parameters gives, i) a value of the distorsion which agreeswell with some recent estimate for a lower bound, we are able to perfectly reproduce ii)the dispersions, iii) the experimental susceptibility at both high and low temperatures. By performing DMRG calculations for 2 coupled chains we have analysed the effect of the transverse coupling on the ratio of singlet to triplet gaps. The ratio is very sensitive to the parameters and the universality reported in the strict one dimensional case is lost. As an additional point, we provide a simple picture to explain the interesting new feature observed in recent inelastic neutron scattering experiments: the existence of a second branch of excitations.