次维临界性：X立方体模型中的线子和平面子的凝聚
Subdimensional criticality: condensation of lineons and planons in the X-cube model
摘要：
研究了$\mathbb{Z}_N$ X立方体模型中分形有序相的量子相变。这些相变发生时，各种类型的子维激发和它们的复合物凝聚。凝聚相要么是平凡的顺磁体，要么是由$d=2$或$d=3$去精细规范理论的叠加构成的，其中$d$是空间维度。相变的性质取决于被压缩的激发。在凝聚偶极束缚态的分形子或线子，为$N \geq 4$，我们发现稳定的临界点描述的解耦堆栈的$d=2$共形场论。在凝聚线子激发时，当$N > 4$时，我们发现X立方和凝聚相之间的无隙相中间体，描述为$d=1$共形场论的阵列。在所有这些情况下，有效的子系统的对称性产生的流动性约束的激发的X-立方相，并发挥了重要的作用，在分析的相变。
英文摘要：
We study quantum phase transitions out of the fracton ordered phase of the $\mathbb{Z}_N$ X-cube model. These phase transitions occur when various types of sub-dimensional excitations and their composites are condensed. The condensed phases are either trivial paramagnets, or are built from stacks of $d=2$ or $d=3$ deconfined gauge theories, where $d$ is the spatial dimension. The nature of the phase transitions depends on the excitations being condensed. Upon condensing dipolar bound states of fractons or lineons, for $N \geq 4$ we find stable critical points described by decoupled stacks of $d=2$ conformal field theories. Upon condensing lineon excitations, when $N > 4$ we find a gapless phase intermediate between the X-cube and condensed phases, described as an array of $d=1$ conformal field theories. In all these cases, effective subsystem symmetries arise from the mobility constraints on the excitations of the X-cube phase and play an important role in the analysis of the phase transitions.
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