论文标题
奇怪的分区理论，近端命令和帕顿构造
Odd Fracton Theories, Proximate Orders, and Parton Constructions
论文作者
论文摘要
Lieb-Schultz-Mattis（LSM）定理意味着，当晶格翻译和$ u（1）$对称性的组合结合时，物质的间隙阶段必须满足其低能特性的非平凡条件。我们描述了一个框架，以表征对称性对分形和其他亚比分数激发的作用，并将其与LSM定理一起使用，以确定只能在整数或半模具填充物上发生X-Cube Fracton Order。使用显式的Parton构造，我们证明了X-Cube Fracton顺序的“奇数”版本可以在Half-Odd-Integer填充的系统中发生，从而将奇数$ z_2 $量规理论的概念推广到fracton设置。在一半的填充物上，通过凝结分数准粒子来退出X立方相，从而导致对称性破坏，从而使我们能够识别一类传统的有序相位，即与Fracton Order相关的相位。我们利用对这些有序阶段之一的双重描述，表明其拓扑缺陷自然具有限制的活动能力。然后，这些缺陷的凝结对导致了一个阶段，其激发继承了这些移动性限制。
The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy non-trivial conditions on their low-energy properties when a combination of lattice translation and $U(1)$ symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other sub-dimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that "odd" versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd $Z_2$ gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry-breaking, thereby allowing us to identify a class of conventional ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. Condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.
