高阶对称$U(1)$规范理论中的Higgs机制
The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
摘要：
我们使用希格斯机制调查高阶对称$U(1)$规范理论和带隙分形子相位之间的联系。我们定义了两类秩为2的对称$U(1)$规范理论：$(m,n)$标量和矢量电荷理论，整数$m$和$n$，尊重对称的正方形（立方）晶格在两（三）个空间维度。我们进一步提供了本地晶格转子模型，其低能量动力学描述这些理论。然后，我们详细描述了希格斯相位时得到的$U(1)$规范对称性自发破缺的离散子群。标量电荷理论的一个子集确实有X-cube分数阶作为它们的希格斯相，虽然我们发现，这只能发生在连续高阶规范理论打破连续空间旋转对称性的情况下。然而，并不是所有的高阶规范理论都有分形希格斯相;其他希格斯相具有传统的拓扑序。然而，他们产生有趣的新的传统拓扑秩序的精确可解模型，有点让人想起在两个和三个空间维度的颜色代码模型。我们还研究了这些模型中的相变，并发现了一个可能的直接相变之间的四个副本的$\mathbb{Z}_2$规范理论在三个空间维度和X立方分数阶。
英文摘要：
We use the Higgs mechanism to investigate connections between higher-rank symmetric $U(1)$ gauge theories and gapped fracton phases. We define two classes of rank-2 symmetric $U(1)$ gauge theories: the $(m,n)$ scalar and vector charge theories, for integer $m$ and $n$, which respect the symmetry of the square (cubic) lattice in two (three) spatial dimensions. We further provide local lattice rotor models whose low energy dynamics are described by these theories. We then describe in detail the Higgs phases obtained when the $U(1)$ gauge symmetry is spontaneously broken to a discrete subgroup. A subset of the scalar charge theories indeed have X-cube fracton order as their Higgs phase, although we find that this can only occur if the continuum higher rank gauge theory breaks continuous spatial rotational symmetry. However, not all higher rank gauge theories have fractonic Higgs phases; other Higgs phases possess conventional topological order. Nevertheless, they yield interesting novel exactly solvable models of conventional topological order, somewhat reminiscent of the color code models in both two and three spatial dimensions. We also investigate phase transitions in these models and find a possible direct phase transition between four copies of $\mathbb{Z}_2$ gauge theory in three spatial dimensions and X-cube fracton order.
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