ALGEBRAIC BETHE ANSATZ APPROACH TO CORRELATION FUNCTIONS: FROM EXACT REPRESENTATIONS ON THE LATTICE TO ASYMPTOTIC BEHAVIOR

We review recent results concerning the computation, from first principles, of correlation functions of quantum integrable systems. On the example of the XXZ Heisenberg chain, we first recall how to obtain, in the algebraic Bethe Ansatz framework, exact representations for the two-point functions in the finite chain. We then explain how to analyze these expressions so as to derive, in the thermodynamic limit and in the massless regime of the chain, the long distance asymptotic behavior of these two-point functions, hence confirming, at leading order, the Luttinger liquid and conformal field theory predictions.