Quantum criticality in the presence of strong quenched randomness remains a challenging topic in modern condensed matter theory. We show that the topology and anomaly associated with average symmetry can be used to predict certain nontrivial universal properties. Our focus is on systems subject to average Lieb--Schultz--Mattis constraints, where lattice translation symmetry is preserved only on average, while on-site symmetries remain exact. We argue that in the absence of spontaneous symmetry breaking and intrinsic topological order, the system must exhibit critical correlations of local operators in two distinct ways: (i) for some operator $O_e$ charged under exact symmetries, the first absolute moment correlation $\overline{|\langle O_e(x)O^{\dagger}_e(y)\rangle|}$ decays slowly; and (ii) for some operator $O_a$ charged under average symmetries, the first-moment correlation $\overline{\langle O_a(x)O^{\dagger}_a(y)\rangle}$ decays slowly. We verify these predictions in a few examples: the random-singlet Heisenberg spin chain in one dimension, and the disordered free-fermion critical states in symmetry class BDI in one and two dimensions. Surprisingly, even for these well-studied systems, our anomaly-based argument reveals critical correlations overlooked in previous literature. We also discuss the experimental feasibility of measuring these critical correlations.
Criticality of rumor propagation on small-world networks
我们表明，一个简单的模型传播的谣言的小世界网络表现出临界行为在有限的随机性的基础图形。这种转变发生在谣言在其起源的一个小社区“死亡”的政权和谣言在整个人口的有限部分传播的政权之间。通过有限尺寸标度分析计算了临界指数，并研究了临界随机性与网络连通性的关系。这个系统的行为作为网络随机性的函数，与最近报道的流行病模型有着明显的相似之处[M。Kuperman和G. Abramson，Phys. Rev. Lett. 86，2909（2001）]，尽管在各自的动力学规则的实质性差异。
Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions
Unconventional quantum criticality in the kicked rotor
$d$非公度频率驱动的量子反冲转子（QKR）实现了$d$维无序金属的普适类.对于$d>3$，该系统表现出安德森金属-绝缘体转变，已观察到的原子光学实现的框架内。然而，在QKR中缺乏真正的随机性反映在安德森普适类之外的临界现象中。具体地说，该系统表现出很强的敏感性，其有效普朗克常量$\tilde h \equiv 4π/q$的代数性质。对于整数$q$，系统可能处于全局可积状态，处于以发散响应系数为特征的“超金属”构型，安德森局域化，金属化，或表现出这些相之间的转变。我们提出了不同的$q$值和有效的维数的数值数据，重点是参数配置，可以访问实验研究。
Decoherence-induced self-dual criticality in topological states of matter
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；University of Geneva（日内瓦大学）；University of Cologne（科隆大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
