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

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.