Practical solution to the Monte Carlo sign problem: Realistic calculations of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$

We present a practical solution to the ‘‘sign problem’’ in the auxiliary field Monte Carlo approach to the nuclear shell model. The method is based on extrapolation from a continuous family of problem-free Hamiltonians. To demonstrate the resultant ability to treat large shell-model problems, we present results for the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ in the full fp-shell basis using the Brown-Richter interaction. We find the Gamow-Teller ${\mathrm{\beta }}^{+}$ strength to be quenched by 58% relative to the single-particle estimate, in better agreement with experiment than previous estimates based on truncated bases.