Scaling of excitations in dimerized and frustrated spin-(1/2) chains

We study the finite-size behavior of the low-lying excitations of spin-(1/2) Heisenberg chains with dimerization and next-to-nearest neighbors interaction J{sub 2}. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results and shows that, for different values of the dimerization parameter {delta}, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of l=L/{xi} (where L is the length of the chain and {xi} is the correlation length). At J{sub 2}=J{sub 2c}, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luescher's theory. For small {delta} we find a very good agreement for l > or approx. 4 or 7 depending on the excitation considered.