The discovery of new materials with properties dominated by strong correlations among electrons has opened the problem of new appropriate calculation schemes. In the case of 1D models the Bethe ansatz provides an exact evaluation of many relevant physical quantities, but not a complete framework. By way of developing new methods appropriate to strongly correlated systems, we study the 1D Hubbard model by means of the Composite Operator Method. We investigate various local quantities. A comparison with exact results and other analytical approaches show a reasonable agreement and determine the applicability range of our approximate scheme.
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