Neural Quantum States of frustrated magnets: generalization and sign structure
Neural Quantum States of frustrated magnets: generalization and sign structure
复制标题
受挫磁体的神经量子态：概括和符号结构
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
A. Bagrov
中科院分区：
文献类型：
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作者：
T. Westerhout;N. Astrakhantsev;K. Tikhonov;M. Katsnelson;A. Bagrov
神经量子态（NQS）因其作为量子多体系统的极具表现力的变分拟像的潜力而引起了广泛关注。在这里，我们通过训练神经网络来近似几个中等大小的哈密顿量的基态，使用希尔伯特空间基础的一个小子集上的相应波函数结构作为训练数据集，研究控制 NQS 对受挫磁体适用性的主要因素。我们注意到，当挫败感增加时，泛化质量（即从有限数量的样本中学习并正确近似其余空间上的目标状态的能力）会突然下降。我们还表明，学习符号结构比学习振幅要困难得多。最后，我们得出结论，为了使用NQS方法来模拟现实模型，现阶段要解决的主要问题是泛化性而不是可表达性。
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 wavefunction 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.