Abstract:
Simple unitary transformations of the group $U(N)$ that make it possible
to diagonalize the Hamiltonian of an $N$-level quantum system are
proposed. The use of Hubbard operators to construct the generators
of the group ensures the possibility of obtaining in explicit form the
laws of transformation of the Hubbard operators under unitary rotations.
Recursion relations connecting the parameters of the Hamiltonian in the
new basis to its parameters in the original basis are found. The proposed form of the general method of unitary transformations is demonstrated by the example of strongly anisotropic ferromagnets with a large number of levels of magnetoactive ions. The developed approach
has made it possible to trace in a unified manner the transition of
easy-plane ($S=2$) and cubic ($S=4$) ferromagnets to the quadrupole phase with increasing anisotropy constants and to determine the values of these constants.
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