Abstract
The considerations using such quantities like a. o. correlation function (Green function), certain subspace in Hilbert space, have been applied in terms of the mean field theory both to the Hubbard and Heisenberg spin Hamiltonian. This procedure results in that the magnetization of the system under consideration occurs only if the corresponding topological invariants assume special values. Several examples are discussed using this approach for different types of the magnetic ordering. A general hypothesis has been put forward that particular condensed matter phases (not only magnetic) in a given system take place if certain topological invariants of a given subspace defined in the space of states assume special values.
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