# On symmetries of Hamiltonians describing systems with arbitrary spins

## TL;DR

This paper explores the symmetries of Hamiltonians with arbitrary spins, revealing that Bethe ansatz equations correspond to polynomial relations between operator invariants, thus advancing understanding of their solvability.

## Contribution

It establishes an equivalence between Bethe ansatz equations and polynomial relations among operator invariants for systems with SU(2) symmetry.

## Key findings

- Bethe ansatz equations are equivalent to polynomial relations.
- Some Hamiltonians with SU(2) symmetry are exactly solvable.
- Operator invariants' eigenvalues relate to the Bethe ansatz solutions.

## Abstract

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial relationships between the operator invariants, or equivalently, between eigenvalues of those invariants.