Asymptotics and functional form of correlators in the XX - spin chain of finite length

TL;DR

This paper confirms the asymptotic behavior of spin-spin correlation functions in the finite XX spin chain, deriving exact expressions and comparing them with conformal invariance and bosonization predictions, including subleading constants.

Contribution

It provides the exact finite-lattice correlator expression and links the asymptotic constants to previous theoretical proposals, extending understanding of finite-size effects.

Findings

Exact correlator expression for finite XX chain

Excellent agreement with asymptotic predictions at small distances

Identification of constants matching theoretical conjectures

Abstract

We verify the functional form of the asymptotics of the spin - spin equal - time correlation function for the XX-chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that bosonization also predicts the functional form of the correlators for the chains of finite length. We found the exact expression for the spin- spin equal- time correlator on finite lattice. We find the excellent agreement of the exact correlator with the prediction given by the leading asymptotics result up to the very small distances. We also establish the correspondence between the value of the constant before the asymptotics for the XX- chain with the expression for this constant proposed by Lukyanov and Zamolodchikov. We also evaluate the constant corresponding to the subleading term in the asymptotics in a way which is different from the previous studies.