This work proposes Quantum Monte Carlo (QMC) methods for interacting many-fermion systems by leveraging the stochastic gauge freedom, originally developed in Gaussian phase-space QMC, within the phaseless auxiliary-field QMC (AFQMC) framework. In particular, the approach reinterprets the conventional force bias in phaseless AFQMC as a drift gauge and explores Fermi gauges based on the natural orbitals of a reduced one-body density matrix defined via a mixed estimator, yielding stochastic, time-dependent Hartree-Fock-like dynamics. A symmetry-projection sampling scheme is also introduced to improve sampling efficiency. As a proof of concept, these gauge-augmented AFQMC methods are applied to a simple shell-model Hamiltonian: the Lipkin-Meshkov-Glick model. Numerical results illustrate the potential of stochastic gauges to enhance accuracy and reduce fluctuations, underscoring the promise for advancing these techniques toward more realistic shell-model applications.

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• Monte Carlo methods
• Nuclear many-body theory
• Quantum Monte Carlo
• Shell model
• Thermal & statistical models