On the Static Approximation for the Hubbard Model. I. General Considerations

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Abstract
Starting from the functional‐differential equation for the self‐energy, a static approximation is introduced which is shown to be equivalent to the replacement of the Hubbard model by an alloy model. By means of the single‐site coherent potential approximation an equation is derived which determines the distribution function, characterizing this alloy model self‐consistently by the Green's function. The procedure avoids shortcomings of other methods, as ad‐hoc assumptions on the distribution function or non‐unique decompositions of the interaction term.