Dual fermion dynamical cluster approach for strongly correlated systems

Abstract

We have designed a multiscale approach for strongly correlated systems by combining the dynamical cluster approximation (DCA) 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. Short-length-scale physics is addressed by the DCA cluster calculation, while longer-length-scale physics is addressed diagrammatically using dual fermions. The bare and dressed dual fermionic Green functions scale as $\mathcal{O}(1/{L}_{c})$, 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 $\mathcal{O}(1/{L}_{c}^{3})$ with third-order and three-body corrections down by an additional factor of $\mathcal{O}(1/{L}_{c})$.