Exponential Convergence of Cellular Dynamical Mean Field Theory: Reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460)

TL;DR

This paper defends the exponential convergence rate of local observables in Cellular Dynamical Mean Field Theory (CDMFT) for finite correlation lengths, contrasting it with the slower convergence of the DCA, and refutes prior claims.

Contribution

It provides general arguments and explicit examples demonstrating exponential convergence in CDMFT, challenging previous assertions of slower convergence rates.

Findings

Local observables converge exponentially fast in CDMFT for finite correlation length

Exponential convergence rate is faster than the 1/Lc^2 rate of DCA

The central assertion of the comment by Aryanpour et al. is refuted

Abstract

We reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460) on our paper (Phys. Rev. B {\bf 65} 155112 (2002)). We demonstrate using general arguments and explicit examples that whenever the correlation length is finite, local observables converge exponentially fast in the cluster size, $L_{c}$, within Cellular Dynamical Mean Field Theory (CDMFT). This is a faster rate of convergence than the $1/L_{c}^{2}$ behavior of the Dynamical Cluster approximation (DCA) thus refuting the central assertion of their comment.