Exponential Convergence of Cellular Dynamical Mean Field Theory: Reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460)
G. Biroli, G. Kotliar
Abstract
We reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460) on our paper (Phys. Rev. B 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, Lc, within Cellular Dynamical Mean Field Theory (CDMFT). This is a faster rate of convergence than the 1/Lc2 behavior of the Dynamical Cluster approximation (DCA) thus refuting the central assertion of their comment.
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