The Dynamical Cluster Approximation (DCA) versus the Cellular Dynamical Mean Field Theory (CDMFT) in strongly correlated electrons systems

TL;DR

This paper corrects a previous comparison between DCA and CDMFT methods for strongly correlated electron systems, showing that DCA converges faster when implemented properly, contrary to earlier claims.

Contribution

It provides the correct implementation of DCA for a specific model and demonstrates its faster convergence compared to CDMFT, clarifying previous misconceptions.

Findings

Correct DCA implementation shows faster convergence.

Original comparison was based on incorrect DCA implementation.

Cluster-averaged quantities favor DCA when properly calculated.

Abstract

We are commenting on the article Phys. Rev. {\bf B 65}, 155112 (2002) by G. Biroli and G. Kotliar in which they make a comparison between two cluster techniques, the {\it Cellular Dynamical Mean Field Theory} (CDMFT) and the {\it Dynamical Cluster Approximation} (DCA). Based upon an incorrect implementation of the DCA technique in their work, they conclude that the CDMFT is a faster converging technique than the DCA. We present the correct DCA prescription for the particular model Hamiltonian studied in their article and conclude that the DCA, once implemented correctly, is a faster converging technique for the quantities averaged over the cluster. We also refer to their latest response to our comment where they argue that instead of averaging over the cluster, local observables should be calculated in the bulk of the cluster which indeed makes them converge much faster in the CDMFT than in the DCA. We however show that in their original work, the authors themselves use the cluster averaged quantities to draw their conclusions in favor of using the CDMFT over the DCA.