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A diagram technique for Hubbard operators: the magnetic phase diagram in the (t-J) model

The authors construct a diagram technique for the (t-J) model Hamiltonian expressed in terms of Hubbard operators. This technique combines features of the diagram technique for normal Fermi systems and those for the Heisenberg model with spin operators. The general graphic structure is identified for one-particle Green functions composed of Hubbard operators. The (t-J) model has logical consistency, is reasonably simple and can serve as a working tool in exploring various properties of this model. To an approximation that resides in summing ladder-type diagrams with antiparallel electron lines, the authors calculate the system's magnetic susceptibility. A formula is derived which reflects the dual nature of the magnetic states in the Hubbard model; this duality manifests itself in the presence of a localised and an itinerant contribution in the bare susceptibility. The authors trace how the relative value of the localised contribution varies as the electron concentration is increased from 0 to 1. With n>2/3, the paramagnetic phase of the system becomes unstable with respect to the occurrence of ferromagnetic or antiferromagnetic ordering. A magnetic phase diagram for zero temperature is constructed on the (t/U, n) plane.