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

TL;DR

This paper derives the localization length of a soliton caused by a non-magnetic impurity in a double-spin-chain model, revealing a power-law dependence on dimerization and explaining differences in magnetic order in certain materials.

Contribution

It introduces a variational approach using the singlet-dimer basis to analytically determine soliton localization length in a general double-spin-chain model.

Findings

Localization length follows a power law with exponent -1/3.

The model explains the absence of antiferromagnetic order in NaV2O5.

Impurity doping effects differ based on the origin of the gap.

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 $(\xi)$ is found to obey a power law of the dimerization $(J_2-J_3)$ with an exponent -1/3; $\xi\sim (J_2-J_3)^{-1/3}$. 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.