Quantum periodic cluster methods for strongly correlated electron systems

TL;DR

This paper introduces a reformulation of quantum periodic cluster methods for strongly correlated electrons using a canonical transformation, leading to faster convergence and new theoretical insights.

Contribution

The authors develop a canonical transformation-based approach that relates dynamical cluster approximation and cellular dynamical mean field theory, and introduce a periodic cluster perturbation theory with rapid convergence.

Findings

Periodic cluster perturbation theory converges with corrections of order 1/L_c^2.

Canonical transformation relates different cluster methods.

The new approach improves convergence speed in simulations.

Abstract

Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The dynamical cluster approximation and the cellular dynamical mean field theory are related each other through the canonical transformation. A cluster perturbation theory with periodic boundary conditions is developed. It is found that the periodic cluster perturbation theory converges rapidly with corrections $\mathcal{O}(1/L_c^2)$, where $L_c$ is the linear size of the clusters, whereas the ordinary cluster perturbation theory converges with corrections $\mathcal{O}(1/L_c)$.