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Searching magnetic states using an unsupervised machine learning algorithm with the Heisenberg model

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.