On Application of the Jucys–Murphy Operators in the Hubbard Model of Solids

The operator techniques based on the Jucys–Murphy operators are applied in the procedure of an immediate diagonalization of the one-dimensional Hubbard model of solids. The Young orthogonal basis is given by the irreducible basis of the symmetric group acting on the set of nodes of the magnetic chain. An example of the attractive Hubbard model at the half-filled magnetic rings case is considered where the group SU(2)×SU(2) acts within the spin and pseudo-spin space. These techniques significantly reduce the size of eigenproblem of the Hubbard Hamiltonian.