Recent theoretical research on tensor gauge theories led to the discovery of an exotic type of quasiparticles, dubbed fractons, that obey both charge and dipole conservation. Here we describe physical implementation of dipole conservation laws in realistic systems. We show that fractons find a natural realization in hole-doped antiferromagnets. There, individual holes are largely immobile, while dipolar hole pairs move with ease. First, we demonstrate a broad parametric regime of fracton behavior in hole-doped two-dimensional Ising antiferromagnets viable through five orders in perturbation theory. We then specialize to the case of holes confined to one dimension in an otherwise two-dimensional antiferromagnetic background, which can be realized via the application of external fields in experiments, and prove ideal fracton behavior. We explicitly map the model onto a fracton Hamiltonian featuring conservation of dipole moment. Manifestations of fractonicity in these systems include gravitational clustering of holes. We also discuss diagnostics of fracton behavior, which we argue is borne out in existing experimental results.

关于张量规理论的最新理论研究导致发现了一种奇异的准粒子，称为分形子，既服从电荷守恒，又服从偶极守恒。在这里，我们描述了在现实系统中偶极守恒定律的物理实现。我们证明了分数元素在空穴掺杂反铁磁体中找到了自然的实现。在那里，各个孔基本上不动，而偶极孔对则轻松移动。首先，我们证明了在微扰理论中可以通过五个阶生存的空穴掺杂二维Ising反铁磁体中的fracton行为的广义参数范围。然后，我们专门研究在二维反铁磁背景下被限制在一维的孔的情况，这可以通过在实验中应用外部场来实现，并证明理想的fracton行为。我们将模型明确映射到特征为偶极矩守恒的分形哈密顿量。这些系统中分形的表现包括空穴的重力聚集。我们还将讨论fracton行为的诊断，我们认为这已在现有实验结果中得到证实。