On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

TL;DR

This paper analyzes the behavior of specific form factors in the massless XXZ Heisenberg chain as the system size grows large, revealing their decay rates and connection to correlation functions.

Contribution

It provides explicit calculations of form factor decay and relates them to long-distance correlation asymptotics in the thermodynamic limit.

Findings

Form factors decay as a power law with system size

Explicit exponents and amplitudes are computed

Form factors determine leading oscillations in correlation functions

Abstract

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M, and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.