用受限玻尔兹曼机学习自旋玻璃的退化基态，精准捕捉复杂关联特征。
Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines
- 用受限玻尔兹曼机建模受挫磁体的退化基态空间。
- 在1D ANNNI模型和凯姆克自旋冰中准确复现振荡与指数关联。
- 适合研究强关联、对称性破缺的量子磁性系统者阅读。
我们证明受限玻尔兹曼机（RBMs）可作为灵活的生成模型，用于描述受挫磁体中无序但强关联相的自旋构型。以一维ANNNI模型在多相点的零温基态为基准，验证了RBMs能准确复现其特征的振荡与指数衰减关联。随后将方法应用于凯姆克自旋冰，结果表明RBMs成功学习到局部冰规则及短程关联，且由生成构型计算的关联函数与直接蒙特卡洛模拟高度一致。对于部分有序的冰-II相——具有长程电荷序和时间反演对称性破缺——需引入均匀符号偏置场的RBMs才能实现精确建模，这反映了内在对称性破缺。这些结果凸显了RBMs在学习约束性强关联磁性状态中的有效性。
原文摘要 · Abstract (English)
We show that Restricted Boltzmann Machines (RBMs) provide a flexible generative framework for modeling spin configurations in disordered yet strongly correlated phases of frustrated magnets. As a benchmark, we first demonstrate that an RBM can learn the zero-temperature ground-state manifold of the one-dimensional ANNNI model at its multiphase point, accurately reproducing its characteristic oscillatory and exponentially decaying correlations. We then apply RBMs to kagome spin ice and show that they successfully learn the local ice rules and short-range correlations of the extensively degenerate ice-I manifold. Correlation functions computed from RBM-generated configurations closely match those from direct Monte Carlo simulations. For the partially ordered ice-II phase -- featuring long-range charge order and broken time-reversal symmetry -- accurate modeling requires RBMs with uniform-sign bias fields, mirroring the underlying symmetry breaking. These results highlight the utility of RBMs as generative models for learning constrained and highly frustrated magnetic states.
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