Approaches to form-factors of higher spin Heisenberg chains

Abstract

In this thesis we apply the vertex operator approach of Jimbo and Miwa to higher spin Heisenberg chains with the aim of computing the form-factors of these quantum integrable models. The work is motivated by the relation of the form-factors to the dynamical structure factors of the model - objects that are experimentally realisable - and potential for comparison with real-world results. Using a one boson, one fermion free field realisation of Uq(sl2), in conjunction with a realisation for the fermionic contribution due to Shiraishi, we are able to give the formalism required to obtain explicit multiple integral expressions for the 2m-particle form-factors of the antiferromagnetic spin-1 Heisenberg chain. Using this novel boson-fermion-Shiraishi scheme, we are able to obtain single integral expressions for the two-spinon contribution to the S+ form-factor. We also consider a certain modification of a known q-Wakimoto bosonisation scheme for arbitrary spin and its relevance to the computation of higher spin form-factors. We consider the form of the resultant BRST relations and discuss simplifications arising through this approach, as well as the difficulties faced in obtaining integral expressions.