Auxiliary field Monte-Carlo simulation of strong coupling lattice QCD for QCD phase diagram

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We study the QCD phase diagram in the strong coupling limit with fluctuation effects by using the auxiliary field Monte-Carlo method. We apply the chiral angle fixing technique in order to obtain finite chiral condensate in the chiral limit in finite volume. The behavior of order parameters suggests that chiral phase transition is the second order or crossover at low chemical potential and the first order at high chemical potential. Compared with the mean field results, the hadronic phase is suppressed at low chemical potential, and is extended at high chemical potential as already suggested in the monomer-dimer-polymer simulations. We find that the sign problem originating from the bosonization procedure is weakened by the phase cancellation mechanism; a complex phase from one site tends to be canceled by the nearest neighbor site phase as long as low momentum auxiliary field contributions dominate.