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Auxiliary field Monte-Carlo study of the QCD phase diagram at strong coupling

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.