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

摘要

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