卷积限制Boltzmann机辅助Monte Carlo：Ising和Kitaev模型的应用
Convolutional restricted Boltzmann machine aided Monte Carlo: An application to Ising and Kitaev models
摘要：
机器学习在多体凝聚态系统的热力学分析中得到了广泛的应用。受限玻尔兹曼机（RBM）辅助的蒙特卡罗模拟最近引起了人们的兴趣，因为它们设法加速经典的蒙特卡罗模拟。在这里，我们采用卷积限制玻尔兹曼机（CRBM）的方法，并表明它的使用有助于减少要学习的参数的数量，通过利用平移不变性大幅。此外，我们表明，它是可能的训练CRBM在较小的晶格尺寸，并将其应用到较大的晶格尺寸。为了证明CRBM的效率，我们将其应用到范例伊辛和Kitaev模型在二维。
英文摘要：
Machine learning is becoming widely used in analyzing the thermodynamics of many-body condensed matter systems. Restricted Boltzmann Machine (RBM) aided Monte Carlo simulations have sparked interest recently, as they manage to speed up classical Monte Carlo simulations. Here we employ the Convolutional Restricted Boltzmann Machine (CRBM) method and show that its use helps to reduce the number of parameters to be learned drastically by taking advantage of translation invariance. Furthermore, we show that it is possible to train the CRBM at smaller lattice sizes, and apply it to larger lattice sizes. To demonstrate the efficiency of CRBM we apply it to the paradigmatic Ising and Kitaev models in two-dimensions.
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