Correlation Functions as Nests of Self-Avoiding Paths

TL;DR

This paper explores the link between the XXZ Heisenberg spin chain at zero anisotropy and combinatorics, using symmetric functions to derive correlation functions through nests of self-avoiding paths.

Contribution

It introduces a combinatorial approach to calculating dynamical correlation functions using nests of self-avoiding lattice paths, connecting physics and enumerative combinatorics.

Findings

Derived correlation functions via combinatorial methods

Connected Bethe wave functions with symmetric functions

Provided a new combinatorial derivation of dynamical correlations

Abstract

We discuss connection between the XXZ Heisenberg spin chain in the limiting case of zero anisotropy 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 calculation of the correlation functions. We provide a combinatorial derivation of the dynamical correlation functions of the projection operator in terms of nests of self-avoiding lattice paths.