Localization length of a soliton from a nonmagnetic impurity in a general double-spin-chain model

Localization length of a free-spin soliton from a nonmagnetic impurity is deduced in a general double-spin-chain model (Formula presented) model). We have solved a variational problem which employs the nearest-neighbor singlet-dimer basis. The wave function of a soliton is expressed by the Airy function, and the localization length (ξ) is found to obey a power law of the dimerization (Formula presented) with an exponent (Formula presented) (Formula presented) This explains why (Formula presented) does not show the antiferromagnetic order, while (Formula presented) does by impurity doping. When the gap exists by the bond dimerization, a soliton is localized and no order is expected. On the contrary, there is a possibility of the order when the gap is mainly due to frustration.