On form-factor expansions for the XXZ chain in the massive regime

TL;DR

This paper analyzes the large-volume behavior of form factors in the XXZ spin chain's massive regime, deriving a form-factor expansion for two-point correlations and revealing the decay rates of individual form factors.

Contribution

It introduces a detailed analysis of form factors' decay in the XXZ chain and derives a new expansion for two-point correlations in the thermodynamic limit.

Findings

Form factors decay as L^{-n} with n even, related to the number of holes.

The form-factor expansion naturally includes staggered magnetization as the leading term.

Other contributions to correlations decay exponentially at large distances.

Abstract

We study the large-volume-$L$ limit of form factors of the longitudinal spin operators for the XXZ spin-$1/2$ chain in the massive regime. We find that the individual form factors decay as $L^{-n}$, $n$ being an even integer counting the number of physical excitations -- the holes -- that constitute the excited state. Our expression allows us to derive the form-factor expansion of two-point spin-spin correlation functions in the thermodynamic limit $L\rightarrow +\infty$. The staggered magnetisation appears naturally as the first term in this expansion. We show that all other contributions to the two-point correlation function are exponentially small in the large-distance regime.