Localization length of a soliton from a non-magnetic impurity in a general double-spin-chain model
Abstract
A localization length of a free-spin soliton from a non-magnetic impurity is deduced in a general double-spin-chain model (
J
0
−
J
1
−
J
2
−
J
3
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
(
J
2
−
J
3
)
with an exponent -1/3;
ξ∼(
J
2
−
J
3
)
−1/3
. This explains why NaV_2O_5 does not show the antiferromagnetic order, while CuGeO_3 does by impurity doping. When the gap exists by the bond-dimerization, a soliton is localized and no order is expected. Contrary, there is a possibility of the order when the gap is mainly due to frustration.