Nonlocal Unitary Transformation and String Order inS=1/2Heisenberg Chain with Bond Alternation

Abstract

We investigate the ground-state properties of an S =1/2 Heisenberg chain with bond alternation, which reduces to the S =1 antiferromagnetic (AF) chain in a strong coupling limit, using a nonlocal unitary transformation. It is shown that the transformation works well, as in the case of S =1 AF models, and hence it transforms the model into a ferromagnetic model with a Z 2 × Z 2 symmetry. The phase diagram is calculated in the transformed system with string order parameters by a molecular field approximation, and the result is shown to agree essentially with the numerical result obtained by Hida. We also argue the difference between Hida's string order parameter and one corresponding to the S =1 string order parameter of den Nijs and Rommelse.