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

TL;DR

This paper introduces a novel Path Integral Monte Carlo method with a parametrized partition function to accurately compute the energy of normal liquid helium-3, overcoming the fermionic sign problem and matching experimental data.

Contribution

It develops an extended extrapolation strategy based on a parametrized partition function to address the sign problem in fermionic simulations of liquid helium-3.

Findings

Accurate energy per particle results consistent with experiments.

Effective extrapolation method for fermionic systems with superfluidity.

Overcomes the sign problem in Path Integral Monte Carlo simulations.

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 $\xi \geq 0$, 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.