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

## TL;DR

This paper derives the long-distance and long-time asymptotics of dynamical correlation functions in the massless XXZ spin-1/2 chain using form factor expansion, clarifying the role of bound states without relying on field theory assumptions.

## Contribution

It provides a first-principles derivation of asymptotics for the XXZ chain, explicitly identifying contributions from excited states and resolving the role of bound states in the correlation decay.

## Key findings

- Critical exponents and amplitudes characterized the asymptotics.
- Bound states contribute exponentially small terms at large distances.
- Bound states cancel certain power-law contributions, preserving universality.

## 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.