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

Original · EN

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 δ, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of ℓ=L/ξ(where L is the length of the chain and ξis 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 δwe find a very good agreement for ℓ > 4 or 7 depending on the excitation considered.