Behavior of a frustrated quantum spin chain with bond dimerization

We clarified behavior of the excitation gap in a frustrated S = 1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S = 1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully frustrated point, where a localized kink and a freely mobile antikink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. They finally collapse to a local tripler at a sufficient value of the dimerization. The wave function of the bound state, the consequential gap enhancement, and the localization length of the bound state were obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. We also obtained the dispersion relation of the local triplet excitation for the entire phase space. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J(1)-J(2) model, or the frustrated ladder model.