Searching magnetic states using an unsupervised machine learning algorithm with the Heisenberg model
Searching magnetic states using an unsupervised machine learning algorithm with the Heisenberg model
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DOI：
10.1103/physrevb.99.024423
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发表时间：
2019-01-22
影响因子：
3.7
通讯作者：
Won, C.
中科院分区：
文献类型：
--
作者：
Kwon, H. Y.;Kim, N. J.;Won, C.
磁性是自发对称破缺的典型例子。在居里温度以下，磁态的对称性会自发破缺，即使在对称性下哈密顿量是不变的。最近，机器学习算法已成功地用于研究物理学主题。我们应用无监督机器学习算法来寻找海森堡模型的磁基态。使用完全连接的神经网络从随机编码的特征生成自旋配置，并选择磁能作为机器学习过程中要最小化的成本。我们发现，通过无监督学习过程求解的基态与理论解是一致的。此外，我们将结果与传统计算方法的结果进行了比较，发现机器学习算法提供了一种有效的方法来数值求解磁状态。
Magnetism is a canonical example of a spontaneous symmetry breaking. The symmetry of a magnetic state below the Curie temperature is spontaneously broken even though the Hamiltonian is invariant under symmetry. Recently, machine learning algorithms have been successfully utilized to study topics in physics. We applied unsupervised machine learning algorithms to find the magnetic ground states of the Heisenberg model. A fully connected neural network was used to generate the spin configuration from randomly coded features, and the magnetic energy was selected as the cost to be minimized during the machine learning process. We found that ground states solved by the unsupervised learning process are consistent with the theoretical solution. Also, we compared the results with those from traditional computational methods and found that the machine learning algorithm provides an efficient method to solve the magnetic state numerically.