String correlation functions of the spin-1/2 Heisenberg XXZ chain

TL;DR

This paper computes string correlation functions in the spin-1/2 XXZ Heisenberg chain at zero temperature, revealing exact results for small distances and algebraic decay at large distances, connecting to two-point correlations.

Contribution

It provides the first detailed calculation of string correlation functions for the spin-1/2 XXZ chain, combining Bethe Ansatz, exact diagonalization, and field theory.

Findings

Exact results for small-distance string correlations

Asymptotic algebraic decay at large distances

Connection to two-point spin correlations

Abstract

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.