Formfactors and functional form of correlators in the XX spin chain

TL;DR

This paper derives new determinant expressions for formfactors and correlators in the XX spin chain, providing insights into their asymptotic behavior and momentum distribution, highlighting differences from the Luttinger model.

Contribution

It introduces novel determinant formulas for formfactors and correlators in the XX chain, and analyzes the momentum distribution in the XXZ chain, contrasting it with fermionic models.

Findings

New determinant expressions for formfactors and correlators.

The momentum distribution in the XXZ chain differs from the Luttinger model.

Numerical comparison of formfactors and expectation values in the XX chain.

Abstract

We present the new expressions for the formfactors of local operators for the XX - quantum spin chain as a Cauchy determinants. Using the known functional form of the correlator at large distances we propose the new expression for the constant for the asymptotics of the correlator as a Cauchy determinant. We calculate the momentum distribution for the general case of the XXZ spin chain and point out that it is completely different from the Luttinger model (the system of fermions). For the XX chain we compare numerically the value of the lowest formfactor and the expectation value of momentum- zero operators which is determined by the functional form of the correlator.