Local-chemical-potential approach to small-cluster many-body systems

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Abstract
Thermodynamic local-occupation averages and local-number-occupation fluctuations are studied in small-cluster many-body systems by introducing a single-site chemical potential at a particular site. This procedure allows the study of differential properties of thermodynamic functions by providing continuous variation of local occupations. The method, which starts from the quantum-mechanical grand canonical ensemble, gives a criterion to distinguish particular features of the small cluster that are likely to survive in the thermodynamic limit from those discontinuities that are characteristic of the finiteness of the cluster and the resulting discreteness of the energy spectrum. In particular the Mott-insulating state (a discontinuity in the chemical potential at a particular occupation) can be clearly tested this way. Similar indications are obtained for spin-polarized states and for particle-pairing conditions. Two four-site Hubbard-model clusters–a ring and a tetrahedron–are used as examples.

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