Describing the ground states of continuous, real-space quantum many-body systems, like atoms and molecules, is a significant computational challenge with applications throughout the physical sciences. Recent progress was made by variational methods based on machine learning (ML) ansatzes. However, since these approaches are based on energy minimization, ansatzes must be twice differentiable. This (a) precludes the use of many powerful classes of ML models; and (b) makes the enforcement of bosonic, fermionic, and other symmetries costly. Furthermore, (c) the optimization procedure is often unstable unless it is done by imaginary time propagation, which is often impractically expensive in modern ML models with many parameters. The stochastic representation of wavefunctions (SRW), introduced in (Atanasova et al 2023 Nat. Commun. 14 3601), is a recent approach to overcoming (c). SRW enables imaginary time propagation at scale, and makes some headway towards the solution of problem (b), but remains limited by problem (a). Here, we argue that combining SRW with path integral techniques leads to a new formulation that overcomes all three problems simultaneously. As a demonstration, we apply the approach to generalized ‘Hooke’s atoms’: interacting particles in harmonic wells. We benchmark our results against state-of-the-art data where possible, and use it to investigate the crossover between the Fermi liquid and the Wigner molecule within closed-shell systems. Our results shed new light on the competition between interaction-driven symmetry breaking and kinetic-energy-driven delocalization.

中文翻译：

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波函数随机表示中的无行列式和无导数量子蒙特卡洛


描述连续的实空间量子多体系统（如原子和分子）的基态是整个物理科学应用中的重大计算挑战。基于机器学习 （ML） 拟定的变分方法取得了最近的进展。然而，由于这些方法基于能量最小化，因此 ansatzes 必须是双重可微分的。这 （a） 排除了许多强大的 ML 模型类的使用;（b） 使玻色子、费米子和其他对称性的执行成本高昂。此外， （c） 除非通过虚数时间传播完成，否则优化过程通常是不稳定的，这在具有许多参数的现代 ML 模型中通常不切实际地昂贵。（Atanasova et al 2023 Nat. Commun.14 3601） 中介绍的波函数 （SRW） 的随机表示是克服 （c） 的最新方法。SRW 实现了大规模的虚时间传播，并在解决问题 （b） 方面取得了一些进展，但仍然受到问题 （a） 的限制。在这里，我们认为将 SRW 与路径积分技术相结合会产生一种同时克服所有三个问题的新公式。作为演示，我们将该方法应用于广义的“胡克原子”：谐波井中相互作用的粒子。我们尽可能将结果与最先进的数据进行基准测试，并使用它来研究闭壳系统内费米液体和 Wigner 分子之间的交叉。我们的结果为相互作用驱动的对称性打破和动能驱动的离域之间的竞争提供了新的思路。