基于虚构全同粒子和物理信息神经网络对费米系统热力学性质及相变的第一性原理模拟
Ab initio simulations of the thermodynamic properties and phase transition of Fermi systems based on fictitious identical particles and physics-informed neural networks
AI总结：
本研究将虚构全同粒子方法与物理信息神经网络结合，用于推断费米系统热力学性质并捕捉相变，成功模拟了费米-哈伯德模型和幺正极限费米气体，验证了临界温度的普适性。
摘要：
虚构全同粒子热力学已成为克服费米符号问题的有力工具，使得在温稠密物质中对一千个费米子进行高精度模拟成为可能（T. Dornheim等，J. Phys. Chem. Lett. 15, 1305 (2024)）。然而，从大量玻色子扇区的精确数值模拟中推断费米系统的热力学性质仍然面临微妙挑战，尤其是在高量子简并区域以及存在相变的情况下。在本工作中，我们证明，基于对玻色子扇区进行广泛且无符号问题数值模拟所得数据训练的物理信息神经网络（PINNs），为推断费米系统的热力学性质提供了一种有价值的手段。PINNs在捕捉相变方面可发挥特别关键的作用。为阐明虚构全同粒子与PINNs相结合模拟费米系统热力学的 methodology，我们探索了其在现实场景中的应用，包括周期势中的超冷费米气体，以及三维谐振子陷阱中幺正极限下形成的对凝聚相变。对于空间连续的费米-哈伯德模型，我们在此高效且可靠地模拟了数百个费米子。对于幺正极限下的费米气体，基于虚构全同粒子与PINNs相结合的方法，我们确认了临界温度随费米子数增加而变化的普适结果，并与实验观测一致。
英文摘要：
Fictitious identical particle thermodynamics has emerged as a powerful tool to overcome the fermion sign problem, enabling highly accurate simulations of one thousand fermions in warm dense matter (T. Dornheim et al., J. Phys. Chem. Lett. 15, 1305 (2024)). However, inferring the thermodynamic properties of Fermi systems from a large number of exact numerical simulations of the bosonic sector still poses subtle challenges, especially in the regime of high quantum degeneracy and in the presence of phase transitions. In this work, we demonstrate that physics-informed neural networks (PINNs), trained on data from extensive and sign-problem-free numerical simulations of the bosonic sector, offer a valuable means to infer the thermodynamic properties of Fermi systems. PINNs can play a particularly crucial role in capturing phase transitions. To illustrate the methodology of fictitious identical particles combined with PINNs for simulating the thermodynamics of Fermi systems, we explore its application in realistic scenarios, including ultracold Fermi gases in periodic potentials, and phase transitions of pair condensation formed in the unitary limit in a three-dimensional harmonic trap. For the spatially continuous Fermi-Hubbard model, we efficiently and reliably simulated hundreds of fermions here. For the Fermi gas in the unitary limit, based on the fictitious identical particle combined with PINNs, our approach confirms the universal result of the critical temperature with the increasing of the number of fermions, and is consistent with the experimental observations.
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