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