The hallmark of highly frustrated systems is the presence of many states close in energy to the ground state. Fluctuations between these states can preclude the emergence of any form of order and lead to the appearance of spin liquids. Even on the classical level, spin liquids are not all alike: they may have algebraic or exponential correlation decay, and various forms of long wavelength description, including vector or tensor gauge theories. Here, we introduce a classification scheme, allowing us to fit the diversity of classical spin liquids (CSLs) into a general framework as well as predict and construct new kinds. CSLs with either algebraic or exponential correlation-decay can be classified via the properties of the bottom flat band(s) in their soft-spin Hamiltonians. The classification of the former is based on the algebraic structures of gapless points in the spectra, which relate directly to the emergent generalized Gauss's laws that control the low-temperature physics. The second category of CSLs, meanwhile, are classified by the fragile topology of the gapped bottom band(s). Utilizing the classification scheme we construct new models realizing exotic CSLs, including one with anisotropic generalized Gauss's laws and charges with subdimensional mobility, one with a network of pinch-line singularities in its correlation functions and a series of fragile topological CSLs connected by zero-temperature transitions.

中文翻译：

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经典自旋液体的分类：详细的形式主义和示例套件

高度受挫系统的标志是存在许多能量接近基态的状态。这些状态之间的波动可以阻止任何形式的有序的出现，并导致自旋液体的出现。即使在经典水平上，自旋液体也不完全相同：它们可能具有代数或指数相关衰减，以及各种形式的长波长描述，包括矢量或张量规范理论。在这里，我们引入了一种分类方案，使我们能够将经典自旋液体（CSL）的多样性融入到一个通用框架中，并预测和构建新的类型。具有代数或指数相关衰减的 CSL 可以通过其软自旋哈密顿量中底部平带的属性进行分类。前者的分类基于光谱中无间隙点的代数结构，这与控制低温物理的新兴广义高斯定律直接相关。与此同时，第二类 CSL 是根据有隙底带的脆弱拓扑进行分类的。利用分类方案，我们构建了实现奇异 CSL 的新模型，包括具有各向异性广义高斯定律和具有次维迁移率的电荷的模型、在其相关函数中具有夹线奇点网络的模型以及通过零温度连接的一系列脆弱拓扑 CSL 的模型过渡。