Abstract:

Hydrogen and Helium are the two lightest atoms of the periodic table. The large zero-point energy implies for instance that hydrogen-rich materials are strongly affected by quantum fluctuations or that helium-4 is a liquid even at extremely low temperatures. In order to properly describe these systems one should take into account nuclear quantum effects (NQE) and the impact of quantum statistics. The state-of-the-art method to face these challanges is represented by the Imaginary Time Path Integral approach in either its Molecular Dynamics [1] or Monte Carlo [2] version, the latter being in principle able to find an exact solution of the full quantum N-body problem of interest without any empirical input.

In my talk, I will first introduce the theoretical framework of the Path-Integral approach, by showing how we approximate the propagators and how we take into account the permutational exchanges between identical particles.

Then I will present results for different systems. In the first two, that are sulfur hydride (H3S) [3] and water hexamerv[4], we neglect quantum statistics and we only account for NQE; I will show the relevance of NQE compared to classical approximations. Then I will focus on liquid helium-4 [5] and helium-3 [6], where quantum statistics play a major role. I will present results for both systems and in particular I will focus on helium-3 which is a fermion and therefore much more challenging. In this case the fermion sign problem is treated using a novel method [7], that we had to generalise in order to deal with the strong quantum degeneracy case of liquid helium-3.

References:

• M. Ceriotti et al., Efficient stochastic thermostatting of path integral molecular dynamics, J. Chem. Phys. 133, 124104 (2010)
• D. M. Ceperley, Path Integrals in the theory of condensed helium, Rev. Mod. Phys. 67, 279-355 (1995)
• R. Taureau, M. Cherubini, TM et al., Quantum symmetrization transition in superconducting sulfur hydride from quantum Monte Carlo and path integral molecular dynamics, NPJ Computational Materials 10, 56 (2024)
• F. Mohuat, M. Peria, TM et al., Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer, Nature Communications 14, 6930 (2023)
• TM and G. Garberoglio, Revisiting the properties of superfluid and normal liquid 4He using ab initio potentials, arXiv:2501.08730 (accepted in the Journal of Low Temperature Physics)
• TM and G. Garberoglio, Normal liquid 3He studied by Path Integral Monte Carlo with a parametrized partition function, Phys. Rev. B 111, 014521 (2025)
• Y. Xiong and H. Xiong, On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem, J. Chem. Phys. 157, 094112 (2022)

Biography:

Tommaso Morresi, after graduating at the University of Camerino （Italy） in 2015, obtained his PhD at the University of Trento Italy) with a thesis entitled: “From atoms to extended structures via ab-initio and multi-scale simulations”. In 2019 he moved to Paris (France), for a first post-doc position at Sorbonne University under the supervision of Dr. Michele Casula where he got acquainted with Quantum Monte Carlo and Path Integral methods. In 2022 he moved back to Trento where he is now a post-doc researcher at the European Center for Theoretical Studies in Nuclear Physics and Related Areas. He is currently collaborating with Dr. Giovanni Garberoglio on the solution to the fermion sign problem using fictitious identical particles.