Dual Fermion Dynamical Cluster Approach for Strongly Correlated Systems

TL;DR

The paper introduces a multi-scale approach combining the Dynamical Cluster Approximation and dual-fermion formalism to efficiently study strongly correlated systems across different length scales.

Contribution

It presents a novel method that integrates DCA and dual fermions, enabling accurate treatment of short- and long-range physics with rapid convergence.

Findings

Dual fermion self-energy scales as O(1/Lc^3) with second order perturbation.

Perturbation theory on the dual lattice converges quickly due to Green function scaling.

The approach effectively captures multi-scale physics in strongly correlated systems.

Abstract

We have designed a new multi-scale 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 Lc 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 O(1/Lc) 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 O(1/Lc^3), with third order and three body corrections down by an additional factor of O(1/Lc^2).