量子多体问题的随机抽样神经网络

Chen-yu Liu, Da-wei Wang
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引用次数: 2

摘要

量子多体系统的特征值问题是凝聚态物理中的一个基础和具有挑战性的课题,因为希尔伯特空间的维度(以及所需的计算内存和时间)随着系统尺寸的增加而呈指数增长。一些数值方法已经发展为某些特定的系统,但可能并不适用于其他。本文提出了一种通用的数值方法——随机抽样神经网络(RSNN),通过自监督学习方法,利用模式识别技术对相互作用多体系统的随机抽样矩阵元素进行识别。利用具有横向场的Ising模型、Fermi-Hubbard模型和自旋-$1/2$ $XXZ$模型等精确可解的一维模型对RSNN的适用性进行了验证。即使在弱相互作用区训练相应的RSNN模型,在强相关区或量子相变点附近也能获得相当高的能谱、磁化和临界指数等精度。所需的计算时间与系统大小成线性关系。我们的研究结果表明,将现有的训练过程数值方法和RSNN相结合,可以在更广泛的参数范围内探索量子多体问题,甚至对于强相关系统也是如此。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Random sampling neural network for quantum many-body problems
The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as the system size increases. A few numerical methods have been developed for some specific systems, but may not be applicable in others. Here we propose a general numerical method, Random Sampling Neural Networks (RSNN), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach. Several exactly solvable 1D models, including Ising model with transverse field, Fermi-Hubbard model, and spin-$1/2$ $XXZ$ model, are used to test the applicability of RSNN. Pretty high accuracy of energy spectrum, magnetization and critical exponents etc. can be obtained within the strongly correlated regime or near the quantum phase transition point, even the corresponding RSNN models are trained in the weakly interacting regime. The required computation time scales linearly to the system size. Our results demonstrate that it is possible to combine the existing numerical methods for the training process and RSNN to explore quantum many-body problems in a much wider parameter regime, even for strongly correlated systems.
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