Hidden fermionic structure in quantum integrable models
Fedor Smirnov
LPTHE
Vendredi 25/01/2008, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
We consider critical XXZ model with anisotropy $\Delta =(q+q^{-1})/2$,
$|q|=1$. For this model we study the space of quasi-local
operators $q^{2\alpha S(0)}\mathcal{O}$ with $S(0)=\textstyle
{\frac 1 2}\sum _{j=-\infty}^0\sigma ^3 _j$ and $\mathcal{O}$
localized on finite number of cites. We explain that this space
is created from the primary field $q^{2\alpha S(0)}$ by
two fermions. Similarly to Baxter's $Q$-operator,
these fermions are constructed using $q$-oscillators
representations of quantum affine algebra.
The Vacuum Expectation Values in the fermionic
basis are given by determinants, like in the free theory.