Normal liquid He3 studied by path-integral Monte Carlo with a parametrized partition function

We compute the energy per particle of normal liquid 3 He in the temperature range 0.15–2 K using path-integral Monte Carlo simulations, leveraging a recently proposed method to overcome the sign problem—a long-standing challenge in many-body fermionic simulations. This approach is based on introducing a parameter 𝜉 into the partition function, which allows a generalization from bosons (𝜉=1) to fermions (𝜉=−1). By simulating systems with 𝜉≥0, where the sign problem is absent, one can then extrapolate to the fermionic case at 𝜉=−1. Guided by an independent-particle model that uncovers nonanalytic behavior due to the superfluid transition, which is moderated by finite-size effects, we develop a tailored extrapolation strategy for liquid 3 He that departs from the extrapolation schemes shown to be accurate in those cases where quantum degeneracy effects are weak, and enables accurate results in the presence of Bose-Einstein condensation and superfluidity for 𝜉>0. Our approach extends the previously proposed framework and yields energy per particle values in good agreement with experimental data.