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We discuss the Auxiliary Field Quantum Monte Carlo (AFQMC) method applied todilute neutron matter at finite temperatures. We formulate the discreteHubbard-Stratonovich transformation for the interaction with finite effectiverange which is free from the sign problem. The AFQMC results are compared withthose obtained from exact diagonalization for a toy model. Preliminarycalculations of energy and chemical potential as a function of temperature arepresented.

Quantum Monte Carlo method applied to strongly correlated dilute fermi gases with finite effective range