Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain

Abstract

Starting from the massless form factor expansion for the two-point dynamical correlation functions obtained recently, I extract the long-distance and large-time asymptotics of these correlators. The analysis yields the critical exponents and associated amplitudes characterising the asymptotics. The results are obtained on the basis of exact and first principle based considerations: they \textit{do not rely, at any stage}, on some hypothetical correspondence with a field theory or the use of any other phenomenological approach. Being based on form factor expansion, the method allows one to clearly identify which contributions to the asymptotics issues from which class of excited states. All this permits to settle the long-standing question of the contribution of bound states to the asymptotics of two-point functions. For instance, when considering the long-distance $m$ behaviour of equal-time correlators, the analysis shows that while, \textit{in fine}, the bound states only produce contributions that are exponentially small in $m$, they also play a key role in cancelling out certain power-law contributions which, should they be present, would break explicitly the universality structure of the long-distance behaviour.