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 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 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 ξ is the correlation length). At J 2= J 2 c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Lüscher’s theory. For small δ we find a very good agreement for l≳ 4 or 7 depending on the excitation considered.
American Physical Society
17 Nov 2005
Volume: 72 Issue: 17 Pages: 172409
Physical Review B