Poisson Approximation to a Functional Approach for the Hubbard Model

In a previous paper the Green function for the Hubbard model is represented by a functional average of the Green function for an electron moving in a local time dependent potential Uv i ( t ) taking only the values 0 and U . Here this functional average is calculated with an ad hoc assumed Poisson distribution governing the jumps of Uv i ( t ). In a single‐site approximation the Poisson average can be calculated exactly and leads to a self‐consistent ‚dynamic’ scheme interpolating between band and atomic limit. For a half‐filled band in the paramagnetic case at zero temperature for strong Coulomb repulsion U ≈ 2 two subbands are obtained separated by a minimum of the density of states.