  We investigate the QCD phase diagram in the strong coupling limit by using a
newly developed auxiliary field Monte-Carlo (AFMC) method. Starting from an
effective action in the leading order of the 1/g^2 and 1/d expansion with one
species of unrooted staggered fermion, we solve the many-body problem exactly
by introducing the auxiliary fields and integrating out the temporal links and
quark fields. We have a sign problem in AFMC, which is different from the
original one in finite density lattice QCD. For low momentum auxiliary field
modes, a complex phase cancellation mechanism exists, and the sign problem is
not serious on a small lattice. Compared with the mean field results, the
transition temperature is found to be reduced by around 10 % and the hadron
phase is found to be extended in the larger chemical potential direction by
around 20 %, as observed in the monomer-dimer-polymer (MDP) simulations.
