Binary trees, coproducts, and integrable systems

Abstract

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.

15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices added

References in corpus (5)

• Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries
• Comodule algebras and integrable systems
• High fidelity state transfer in binary tree spin networks
• Generalization of the linear r-matrix formulation through Loop coproducts
• Loop coproducts

Cited by in corpus (5)

• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Different types of integrability and their relation to decoherence in central spin models
• Hyperfine induced spin and entanglement dynamics in Double Quantum Dots: A homogeneous coupling approach
• Swapping and entangling hyperfine coupled nuclear spin baths
• Unexpected systematic degeneracy in a system of two coupled Gaudin models with homogeneous couplings