We have used the auxiliary-field quantum Monte Carlo (AFQMC) many-body approach on the lattice to study the equation of state for a fermionic impurity interacting with a background sea of spin-polarized fermions. The impurity, or polaron, is an interesting system in both cold atomic and nuclear physics. Our approach is general, and we are able to straightforwardly study the polaron across these regimes. We first study the Fermi polaron at unitarity and for a wide range of scattering lengths, comparing against previous theoretical and experimental studies. We then explore the neutron polaron which has been shown to be a useful constraint for nuclear physics. We have also employed the recently developed parametric matrix model to emulate AFQMC solutions to the two-body problem on the lattice, to accelerate the tuning of our lattice Hamiltonian parameters directly to two-body energies in a periodic box, following Lüscher's formula. Our lattice quantum Monte Carlo results for the polaron in both a cold atomic and nuclear physics context can serve as stringent benchmarks for future theoretical and experimental research.

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• Polarons
• Ab initio calculations
• Nuclear many-body theory
• Quantum Monte Carlo