Towards Classification of Fracton Phases: The Multipole Algebra
Towards Classification of Fracton Phases: The Multipole Algebra
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DOI：
10.1103/physrevx.9.031035
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发表时间：
2019-08-27
影响因子：
12.5
通讯作者：
Gromov, Andrey
中科院分区：
文献类型：
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作者：
Gromov, Andrey
我们提出了一种有效的场论方法来研究分数子相。该方法基于多极代数的概念。它是电荷守恒物质的空间(时间)对称性的延伸，它包括负责守恒电荷密度的多极矩的各种分量的全局对称性。我们解释了如何在代数的作用下构造场论不变量。这些场论一般打破转动不变性，表现出各向异性标度。我们进一步解释了如何部分度量多极代数。这样的测量使得对称性负责保持多极矩的局部守恒，同时保持旋转和平移对称性的全局。结果表明，在这种规范下，可以发现对称张量规范理论，以及最近文献中讨论的广义规范理论。我们把所有这样的理论称为多极规范理论。测量过程的结果取决于多极代数的选择。特别地，我们展示了如何基于对称性原理为U(1)型Haah码构造一个有效的理论，并提供了一个具有Sierpinski三角形上的算子的二维例子。我们发现，在带电激发凝聚时，出现了两种类型的分数子相以及各种对称性保护的拓扑相。最后，讨论了该方法与基于有限域上多项式的形式化之间的关系。
We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for the conservation of various components of the multipole moments of the charge density. We explain how to construct field theories invariant under the action of the algebra. These field theories generally break rotational invariance and exhibit anisotropic scaling. We further explain how to partially gauge the multipole algebra. Such gauging makes the symmetries responsible for the conservation of multipole moments local, while keeping rotation and translations symmetries global. It is shown that upon such gauging one finds the symmetric tensor gauge theories, as well as the generalized gauge theories discussed recently in the literature. We refer to all such theories as multipole gauge theories. The outcome of the gauging procedure depends on the choice of the multipole algebra. In particular, we show how to construct an effective theory for the U(1) version of the Haah code based on the principles of symmetry and provide a two-dimensional example with operators supported on a Sierpinski triangle. We show that upon condensation of charged excitations, fracton phases of both types as well as various Symmetry-protected topological phases emerge. Finally, the relation between the present approach and the formalism based on polynomials over finite fields is discussed.