Normal liquid $^3$He studied by Path Integral Monte Carlo with a parametrized partition function
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912227843375104 |
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| author | Morresi, Tommaso Garberoglio, Giovanni |
| author_facet | Morresi, Tommaso Garberoglio, Giovanni |
| contents | 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 $ξ\geq 0$, 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 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 $ξ> 0$. Our approach extends the previously proposed framework and yields energy per particle values in good agreement with experimental data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_01569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal liquid $^3$He studied by Path Integral Monte Carlo with a parametrized partition function Morresi, Tommaso Garberoglio, Giovanni Quantum Gases Materials Science 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 $ξ\geq 0$, 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 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 $ξ> 0$. Our approach extends the previously proposed framework and yields energy per particle values in good agreement with experimental data. |
| title | Normal liquid $^3$He studied by Path Integral Monte Carlo with a parametrized partition function |
| topic | Quantum Gases Materials Science |
| url | https://arxiv.org/abs/2410.01569 |