Classes of integrable spin systems

Abstract

We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two uniformly coupled or disjoint subsystems with property $P$. For these systems the time evolution can be explicitely calculated. The second class consists of spin systems where all non-zero coupling constants have the same strength (spin graphs) possessing $N-1$ independent, commuting constants of motion of Heisenberg type. These systems are shown to have the above property $P$ and can be characterized as spin graphs not containing chains of length four. We completely enumerate and characterize all spin graphs up to N=5 spins. Applications to the construction of symplectic numerical integrators for non-integrable spin systems are briefly discussed.

References in corpus (6)

• Integrability of a disordered Heisenberg spin-1/2 chain
• Fourier law in the alternate mass hard-core potential chain
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems
• Symplectic integrators for classical spin systems
• Classification of integrable clusters of classical Heisenberg spins

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• Lyapunov instabilities in lattices of interacting classical spins at infinite temperature
• Different types of integrability and their relation to decoherence in central spin models
• Symplectic integrators for classical spin systems
• Binary trees, coproducts, and integrable systems
• Evolution of the thermodynamic properties and inelastic neutron scattering intensities for spin-1/2 antiferromagnetic quantum rings
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Thermodynamics of the spin square
• Analytical solutions of symmetric isotropic spin clusters
• Lindblad quantum dynamics from correlation functions of classical spin chains