Symmetry fractionalization in the gauge mean-field theory of quantum spin ice
Symmetry fractionalization in the gauge mean-field theory of quantum spin ice
复制标题
量子自旋冰规范平均场理论中的对称分异
作者：
Félix Desrochers;Li Ern Chern;Yong Baek Kim
对称性分数化是拓扑有序态的一个普遍存在的特征，它可以用来对不同的富对称性拓扑相进行分类，并揭示它们的一些独特的实验特征。尽管它非常受欢迎，但目前还没有可用的框架来研究量子自旋冰（QSI）的对称性分形-在烧绿石晶格上支持出射光子的$U（1）$量子自旋液体（QSL）-在最广泛使用的理论框架中描述它，规范平均场理论（GMFT）。在这项工作中，我们提供了一个扩展的GMFT，允许分类的时空对称性细分。该构造将所有产生在给定对称性和特定低能规范结构下不变的物理波函数的GMFT Ans“atze分类。作为该框架的一个应用，我们首先证明了具有突现U（1）$规范场且遵守所有空间群对称性的仅有的两个Ans“ze是著名的0-和$pi$-通量态。然后，我们展示了如何的框架可以描述QSL超越目前已知的分类手性U（1）$ QSI。我们发现两个新的状态描述的$PI/2$-和$3PI/2$-通量的紧急规范场线程的烧绿石晶格的六边形斑块。最后，我们讨论了如何不同的方式平移对称性的所有这些状态的分形导致独特的实验相关的签名和计算各自的非弹性中子散射截面来说明的论点。
Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) -- a $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons -- within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ans"atze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ans"atze with emergent $U(1)$ gauge fields that respect all space-group symmetries are the well-known 0- and $pi$-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral $U(1)$ QSI. We find two new states described by $pi/2$- and $3pi/2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument.