Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains

TL;DR

This paper introduces a recursion relation that constructs long-range integrable spin chain Hamiltonians, generalizing known models and providing insights into their deformation parameters and Bethe equations, relevant for string/gauge duality.

Contribution

It presents a novel integrability-preserving recursion method for constructing long-range spin chains from nearest-neighbour models, expanding understanding of their moduli space.

Findings

Derived explicit recursion relation for long-range spin chains.

Generalized Haldane-Shastry and Inozemtsev models.

Obtained closed chain asymptotic Bethe equations.

Abstract

We present an integrability-preserving recursion relation for the explicit construction of long-range spin chain Hamiltonians. These chains are generalizations of the Haldane-Shastry and Inozemtsev models and they play an important role in recent advances in string/gauge duality. The method is based on arbitrary nearest-neighbour integrable spin chains and it sheds light on the moduli space of deformation parameters. We also derive the closed chain asymptotic Bethe equations.