Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 106, 35 pages      arXiv:2112.04733      https://doi.org/10.3842/SIGMA.2021.106
Contribution to the Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan

How to Draw a Correlation Function

Nikolay Bogoliubov and Cyril Malyshev
St.-Petersburg Department of Steklov Institute of Mathematics, RAS, Fontanka 27, St.-Petersburg, Russia

Received June 05, 2021, in final form December 02, 2021; Published online December 09, 2021

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.

Key words: $XX0$ Heisenberg spin chain; correlation functions; enumerative combinatorics.

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