Asymptotic behaviour of two-point functions in multi-species models

TL;DR

This paper investigates the long-distance asymptotics of two-point functions in multi-species massless quantum integrable models, extending form factor re-summation methods and confirming critical exponents in specific models.

Contribution

It extends the form factor re-summation method to multi-species models and verifies a key hypothesis using the $SU(3)$-invariant XXX magnet, confirming known critical exponents.

Findings

Validated the large-volume behaviour hypothesis for form factors.

Confirmed the structure of critical exponents in multi-species models.

Extended asymptotic analysis techniques to more complex integrable systems.

Abstract

We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the $SU(3)$-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.