Heisenberg model in pseudo-Euclidean spaces

TL;DR

This paper extends the classical Heisenberg spin chain model to pseudo-Euclidean spaces, demonstrating its Hamiltonian integrability and introducing a new integrable discrete contact system on light-like cones.

Contribution

It constructs and proves the integrability of Heisenberg models on pseudo-spheres and light cones in pseudo-Euclidean spaces, including a novel discrete contact system.

Findings

Heisenberg models on pseudo-spheres are Hamiltonian integrable.

New integrable discrete contact system on light-like cones.

Extension of classical models to pseudo-Euclidean geometries.

Abstract

We construct analogues of the classical Heisenberg spin chain model (or the discrete Neumann system) on pseudo-spheres and light-like cones in the pseudo-Euclidean spaces and show their complete Hamiltonian integrability. Further, we prove that the Heisenberg model on a light--like cone leads to a new example of integrable discrete contact system.