Normal liquid <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math> studied by path-integral Monte Carlo with a parametrized partition function

Abstract

We compute the energy per particle of normal liquid $^{3}\mathrm{He}$ 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 $\ensuremath{\xi}$ into the partition function, which allows a generalization from bosons ($\ensuremath{\xi}=1$) to fermions ($\ensuremath{\xi}=\ensuremath{-}1$). By simulating systems with $\ensuremath{\xi}\ensuremath{\ge}0$, where the sign problem is absent, one can then extrapolate to the fermionic case at $\ensuremath{\xi}=\ensuremath{-}1$. 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 $^{3}\mathrm{He}$ 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 $\ensuremath{\xi}&gt;0$. Our approach extends the previously proposed framework and yields energy per particle values in good agreement with experimental data.

Topics & Concepts