Abstract
A numerically implementable Multi-scale Many-Body approach to
strongly correlated electron systems is introduced. An extension to
quantum cluster methods, it approximates correlations on any given
length-scale commensurate with the strength of the correlations on
the respective scale. Short length-scales are treated
explicitly, long ones are addressed at a mean-field level and
intermediate length-regime correlations are assumed to be
weak and are approximated diagrammatically. To illustrate and
test this method, we apply it to the one dimensional Hubbard model.
The resulting multi-scale self-energy provides a very good
quantitative agreement with substantially more numerically expensive,
explicit Quantum Monte-Carlo calculations.
