How to Draw a Correlation Function

TL;DR

This paper explores the connection between the XX0 Heisenberg spin chain and combinatorics, using symmetric functions to derive and analyze correlation functions with asymptotic behavior in large-scale limits.

Contribution

It introduces a combinatorial approach to calculating auto-correlation functions of the spin chain using Schur functions and lattice path visualization.

Findings

Derivation of dynamical auto-correlation functions via combinatorics

Visualization of correlation functions as nests of lattice paths

Asymptotic behavior characterized in the double scaling limit

Abstract

We discuss connection between the XX0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows to apply the theory of symmetric functions to the calculation of the correlation functions. We provide a combinatorial derivation of the dynamical auto-correlation functions and visualise them in terms of nests of self-avoiding lattice paths. Asymptotics of the auto-correlation functions are obtained in the double scaling limit provided that the evolution parameter is large.