Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down. We illustrate the method with several examples where interactions play a dominant role: systems near metal-insulator transition, systems near volume collapse transition, and systems with local moments.

Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative and are always in the thermodynamic limit. Their quality can be systematically improved, and they provide complementary information to finite size simulations. They have been studied intensively in recent years and are now well established. After a brief historical review, this article comparatively discusses the nature and advantages of these cluster techniques. Applications to common models of correlated electron systems are reviewed.