The burgeoning field of “fractons,” a class of models where quasiparticles are strictly immobile or display restricted mobility that can be understood through generalized multipolar symmetries and associated conservation laws, is reviewed. With a focus on merely a corner of this fast-growing subject, it is demonstrated how one class of such theories, symmetric tensor and coupled-vector gauge theories, surprisingly emerge from familiar elasticity of a two-dimensional quantum crystal. The disclination and dislocation crystal defects, respectively, map onto charges and dipoles of the fracton gauge theory. This fracton-elasticity duality leads to predictions of fractonic phases and quantum phase transitions to their descendants that are duals of the commensurate crystal, supersolid, smectic, and hexatic liquid crystals, as well as amorphous solids, quasicrystals, and elastic membranes. It is shown how these dual gauge theories provide a field-theoretic description of quantum melting transitions through a generalized Higgs mechanism. It is demonstrated how they can be equivalently constructed as gauged models with global multipole symmetries. Extensions of such gauge-elasticity dualities to generalized elasticity theories are expected to provide a route to the discovery of new fractonic models and their potential experimental realizations.

中文翻译：

---

座谈会：分形物质

回顾了新兴的“分形”领域，这是一类模型，其中准粒子严格固定或显示出有限的移动性，可以通过广义多极对称性和相关的守恒定律来理解。仅关注这个快速发展的学科的一个角落，展示了一类这样的理论，对称张量和耦合矢量规范理论，如何令人惊讶地从二维量子晶体的熟悉弹性中出现。向错和位错晶体缺陷分别映射到分形规范理论的电荷和偶极子上。这种分形-弹性二元性导致了分形相和量子相变对其后代的预测，这些后代是相称晶体、超固体、近晶和六方液晶，以及非晶固体、准晶体和弹性膜的对偶。展示了这些双规范理论如何通过广义希格斯机制提供量子熔化跃迁的场论描述。演示了如何将它们等效地构造为具有全局多极对称性的测量模型。将这种规范弹性对偶性扩展到广义弹性理论预计将为发现新的分形模型及其潜在的实验实现提供一条途径。