The effective Hamiltonian method has recently received considerable attention due to its power to deal with finite-temperature problems and large-scale systems. In this work, we put forward a machine learning (ML) approach to generate realistic effective Hamiltonians. In order to find out the important interactions among many possible terms, we propose some new techniques. In particular, we suggest a new criterion to select models with less parameters using a penalty factor instead of the commonly-adopted additional penalty term, and we improve the efficiency of variable selection algorithms by estimating the importance of each possible parameter by its relative uncertainty and the error induced in the parameter reduction. We also employ a testing set and optionally a validation set to help prevent over-fitting problems. To verify the reliability and usefulness of our approach, we take two-dimensional MnO and three-dimensional TbMnO 3 as examples. In the case of TbMnO<...

中文翻译：

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用机器学习方法构造逼真的有效自旋哈密顿量

由于有效的哈密顿方法能够处理有限温度问题和大规模系统，因此最近受到了相当大的关注。在这项工作中，我们提出了一种机器学习（ML）方法来生成逼真的有效哈密顿量。为了找出许多可能的术语之间的重要相互作用，我们提出了一些新技术。特别是，我们提出了一种新的准则，即使用惩罚因子而不是通常采用的附加惩罚项来选择参数较少的模型，并且通过根据每个参数的相对不确定性来估计每个参数的重要性，从而提高变量选择算法的效率。参数减少引起的误差。我们还采用了一个测试集和一个可选的验证集，以帮助防止过度拟合的问题。为了验证我们方法的可靠性和实用性，我们以二维MnO和三维TbMnO 3为例。对于TbMnO <...