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 $q^{2alpha S(0)}mathcal{O}$ with $S(0)=textstyle {frac 1 2}sum _{j=-infty}^0sigma ^3 _j$ and $mathcal{O}$ localized on finite number of cites. We explain that this space is created from the primary field $q^{2alpha S(0)}$ 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.

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