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Quantum evolution of a two-spin system with anisotropic HeisenbergHamiltonian in the magnetic field is considered. We show that this evolutionhappens on some manifold with geometry depending on the ratio between theinteraction couplings and on the initial state. The Fubini-Study metric of thismanifold is calculated. The entanglement of the states belonging to thismanifold is examined. Also we investigate similar problem for a two-spin systemdescribed by the Dzyaloshinsky-Moria Hamiltonian. The problem is solved usingthe fact that this Hamiltonian and the anisotropic Heisenberg Hamiltonian arelinked by the unitary transformation.

Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution