Magnon-magnon interactions in the spin-Peierls compound CuGeO3

In a magnetic substance the gap in the Raman spectrum, Delta(R), and the neutron-scattering gap, Delta(N), are related by Delta(R)/Delta(N) approximate to 2 if the the magnetic excitations (magnons) are only weakly interacting, But for CuGeO3 the experimentally observed ratio is of the order Delta(R)/Delta(N) similar to 1.49-1.78. indicating attractive magnon-magnon interactions in the quasi-one-dimensional spin-Peierls compound CuGeO3. We present numerical estimates of Delta(R)/Delta(N) from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter alpha. An analysis of the numerical Raman intensity leads us to postulate a continuum of two-magnon bound states in the spin-Peierls phase. We discuss in detail the numerical method used. the dependence of the results on the model parameters, and a matrix-element effect due to the dimerization of the Raman operator in the spin-Peierls phase.