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Towards analytical approaches to the dynamical-cluster approximation
I introduce several simplified schemes for the approximation of the
self-consistency condition of the dynamical cluster approximation. The
applicability of the schemes is tested numerically using the
fluctuation-exchange approximation as a cluster solver for the Hubbard model.
Thermodynamic properties are found to be practically indistinguishable from
those computed using the full self-consistent scheme in all cases where the
non-interacting partial density of states is replaced by simplified analytic
forms with matching 1st and 2nd moments. Green functions are also compared and
found to be in close agreement, and the density of states computed using
Pad\'{e} approximant analytic continuation shows that dynamical properties can
also be approximated effectively. Extensions to two-particle properties and
multiple bands are discussed. Simplified approaches to the dynamical cluster
approximation should lead to new analytic solutions of the Hubbard and other
models