Dynamic Spin Correlation Function of the Alternating Spin-1/2 Antiferromagnetic Chain with Competing Interactions

Dynamic spin correlation function of the $S=1/2$ antiferromagnetic spin chain with alternating nearest neighbor and competing next nearest neighbor interactions is studied using the numerical diagonalization method. We find characteristics of the correlation function, which are the consequence of the dimer order in the ground state: (1) A typical singlet-triplet gap is observed and such a lowest-energy triplet state is found to form a bound state, showing strong peaks below a continuum band with weak but distinct upper and lower boundaries. (2) The intensity of the bound state shows a quite different wavevector-dependence from that of the corresponding intensity at the lower boundary in the usual antiferromagnet. These features are examined by the variational calculation and are favorably discussed in connection with recent experimental results of neutron inelastic scattering in the inorganic spin-Peierls system, CuGeO$_3$.