  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.

Strongly Correlated Electrons