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 J2. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results and shows that, for different values of the dimerization parameter d, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of l=L/x (L is the length of the chain and x is the correlation length). At J2 = J2c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luscher's theory. For small d we find a very good agreement for l >= 4 or 7 depending on the excitation considered.