Odd-particle systems in the shell model monte carlo method: circumventing a sign problem

The shell model Monte Carlo method is a powerful technique to calculate thermal and ground-state properties of strongly correlated finite-size systems. However, its application to odd-particle-number systems has been hampered by the sign problem that originates from the projection on an odd number of particles. We circumvent this sign problem for the ground-state energy by extracting the ground-state energy of the odd-particle-number system from the asymptotic behavior of the imaginary-time single-particle Green's function of the even-particle-number system. We apply this method to calculate pairing gaps of nuclei in the iron region. Our results are in good agreement with experimental pairing gaps.