  We study the Hubbard model using the Cellular Dynamical Mean-Field Theory
(CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic
details of CDMFT with the Hirsch-Fye QMC method for the solution of the
self-consistently embedded quantum cluster problem. We use the one- and
two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC
particularly for small clusters by comparing with the exact results and also
with other quantum cluster methods. We calculate single-particle Green's
functions and self-energies on small clusters to study their size dependence in
one- and two-dimensions.
