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.