Data supporting the publication: "Generalization properties of neural network approximations to frustrated magnet ground states"

This repository contains data to reproduce all figures for the paper: "Generalization properties of neural network approximations to frustrated magnet ground states"Tom Westerhout, Nikita Astrakhantsev, Konstantin S. Tikhonov, Mikhail I. Katsnelson & Andrey A. Bagrov Abstract: Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.本仓库包含用于复现论文《神经网络近似对阻挫磁体基态的泛化性质（Generalization properties of neural network approximations to frustrated magnet ground states）》所有图表的数据集，作者为Tom Westerhout、Nikita Astrakhantsev、Konstantin S. Tikhonov、Mikhail I. Katsnelson与Andrey A. Bagrov。 摘要：神经量子态（Neural Quantum States, NQS）凭借其作为量子多体系统极具表现力的变分试探波函数的潜力，受到学界广泛关注。本研究通过训练神经网络，以希尔伯特空间（Hilbert space）基矢的小子集对应的波函数结构作为训练数据集，对若干中等规模哈密顿量的基态进行近似，以此探究制约神经量子态应用于阻挫磁体的核心因素。我们发现，当阻挫程度提升时，泛化性能——即从有限样本中学习并在空间其余部分准确近似目标态的能力——会急剧下降。同时我们证实，相较于学习振幅，学习符号结构的难度显著更高。最终我们得出结论：若要将神经量子态方法用于模拟真实物理模型，当前阶段需要解决的核心问题是泛化性能问题，而非模型的表达能力。