Extended Correlation in Strongly Correlated Systems, Beyond Dynamical Cluster Approximation

We present a new multi-scale approach for strongly correlated systems that combines the Dynamical Cluster Approximation and the recently introduced dual-fermion formalism. This approach employs an exact mapping from a real lattice to a DCA cluster of linear size $L_c$ embedded in a dual fermion lattice. The short-length-scale physics is addressed by DCA cluster calculations, while the longer-length-scale physics is addressed diagrammatically using dual fermions. The bare and dressed dual fermionic Green functions scale as ${\cal{O}}(1/L_c)$, so perturbation theory on the dual lattice converges very quickly. E.g., the dual Fermion self-energy calculated with simple second order perturbation theory is of order ${\cal{O}}(1/L_c^3)$, with third order and three-body corrections down by an additional factor of ${\cal{O}}(1/L_c)$.