Normal liquid ${}^3$He studied by Path Integral Monte Carlo with a parametrized partition function

Abstract

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 $\xi$ into the partition function, which allows a generalization from bosons ($\xi =1$) to fermions ($\xi =-1$). By simulating systems with $\xi \ge 0$, where the sign problem is absent, one can then extrapolate to the fermionic case at $\xi =-1$. Guided by an independent particle model that uncovers non-analytic 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 were quantum degeneracy effects are weak, and enables accurate results in the presence of Bose-Einstein Condensation and superfluidity for $\xi >0$. Our approach extends the previously proposed framework and yields energy per particle values in good agreement with experimental data.

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Cited by in corpus (4)

• Accelerated free energy estimation in ab initio path integral Monte Carlo simulations
• Revisiting the properties of superfluid and normal liquid ${}^4$He using ab initio potentials
• GPU acceleration of ab initio simulations of large-scale identical particles based on path integral molecular dynamics
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem