We design a set of classical macroscopic electric circuits in which charge exhibits the mobility restrictions of fracton quasiparticles. The crucial ingredient in these circuits is a transformer, which induces currents between pairs of adjacent wires. For an appropriately designed geometry, this induction serves to enforce conservation of dipole moment. We show that a network of capacitors connected via ideal transformers will forever remember the dipole moment of its initial charge configuration. Relaxation of the dipole moment in realistic systems can only occur via flux leakage in the transformers, which will lead to violations of fracton physics at the longest times. We propose a concrete diagnostic for these "fractolectric" circuits in the form of their characteristic equilibrium charge configurations, which we verify using simple circuit simulation software. These circuits not only provide an experimental testing ground for fracton physics, but also serve as DC filters. We outline extensions of these ideas to circuits featuring other types of higher moment conservation laws, as well as to higher-dimensional circuits which act as fracton "current-ice." While our focus is on classical circuits, we discuss how these ideas can be straightforwardly extended to realize quantized fractons in superconducting circuits.
Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
我们在$3+1$ D中对由平面子系统对称性保护的子系统对称性保护的拓扑相进行了分类，这些对称性与阿贝尔分形拓扑序是对偶的。我们区分弱SSPT和强SSPT，弱SSPT可以通过堆叠$2+1$ D SPT来构造，强SSPT不能。我们确定强相的签名，并通过明确的建设表明，这样的阶段存在。对任意有限阿贝尔群给出了强相位的一个分类。最后，我们证明了通过$p$ -弦凝聚可实现的分数阶与弱SSPT是对偶的，而强SSPT不允许这样的实现。
Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
物质分形态的发现开启了多体物理学中一个令人兴奋的、基本上尚未探索的领域。某些分形子态与引力的相似性是一个有趣的性质。在早期的工作[H。Yan，Phys. Rev. B 99，155126（2019）]，我们已经证明了反德西特空间中的简单分形模型满足几个主要的全息特性。在这篇后续论文中，我们研究了与原模型对偶的八顶点模型。对偶模型的优点是可以形象地说明互信息和子系统电荷，这有助于揭示它与全息和分形相位研究中的其他各种主题的联系。在零温度下，双八顶点模型是位线模型的离散实现，位线模型是开发用于可视化全息术的强大工具。结合子系统电荷的比特线图像可以定量地描述有限能量下体与边界的等距性，这也是全息术的一个关键问题。黑洞的微观自由度可以在这幅图中被识别出来，它在视界上被非局部地编码。八顶点模型被证明是一个非常有帮助的场所，以提高我们的理解双曲分形模型作为一个玩具模型的全息。
