Quantum fluctuating loops in 2+1 dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins, or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is that the reconnection of a pair of strands is forbidden. This happens at previously-studied multi-critical points between topologically nontrivial phases. We show that this topologically constrained dynamics leads to universality classes with unusual scaling properties. For example, scaling operators at these fixed points are classified by topology, and not only by symmetry. We introduce the concept of the topological operator classification, provide universal scaling forms for correlation functions, and analytical and numerical results for critical exponents. We use an exact correspondence between the imaginary-time dynamics of the 2+1D quantum models and a classical Markovian dynamics for 2D classical loop models with a nonlocal Boltzmann weight (for which we also provide scaling results). We comment on open questions and generalizations of the models discussed for both quantum criticality and classical Markov processes.
Deconfined criticality as intrinsically gapless topological state in one dimension
Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学院和高等研究院）；Department of Physics, Nanjing University（南京大学物理系）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；Harvard University（哈佛大学）；Department of Physics, University of California, San Diego（加州大学圣地亚哥分校物理系）；Fuzhou University（福州大学）；College of Physics and Information Engineering, Fuzhou University（福州大学物理与信息工程学院）
Gauge-constrained Spinon Complexes Near Deconfined Quantum Criticality
University of Tokyo（东京大学）；Institute of Solid-State Physics, University of Tokyo（东京大学固体物理研究所）；Trans-scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）；University of Chongqing（重庆大学）；Department of Physics, University of Chongqing（重庆大学物理学院）
Quantum criticality and factorization in a constrained Rydberg spin chain
School of Systems Science, Beijing Normal University（北京师范大学系统科学学院）；Center for the Cross-disciplinary Research of Space Science and Quantum-technologies (CROSS-Q), College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院空间科学与量子技术交叉研究中心）；National Key Laboratory of Scattering and Radiation（散射与辐射国家重点实验室）
MERA for Spin Chains with Continuously Varying Criticality
本文利用多尺度纠缠重整化方法（MERA）对三个具有Z_2 × Z_2在位对称性的临界量子自旋链：交错XXZ模型、横向场团簇模型和量子Ashkin-Teller模型进行了数值研究。这三种模型都具有连续的单参数临界点族。沿着这条临界线，这些模型的热力学极限预计将由两种可能的c=1共形场论（CFTs）来描述：S^1自由玻色子和它的Z_2轨道。我们的数值计算使用MERA与明确强制的Z_2 x Z_2对称性，使我们能够提取共形数据为每个模型，与强有力的证据支持识别交错XXZ模型和临界横向场集团模型与S^1玻色子CFT，和Ashkin-Teller模型与Z_2-orbifold玻色子CFT。我们的前两个模型描述的相变之间的对称性保护拓扑有序相和平凡相，这是通常的朗道-金斯伯格-威尔逊对称性破缺范式之外。我们的研究结果表明，一系列的临界理论可以出现在一个单一的对称保护相的边界。
Supersymmetric quantum criticality with discrete symmetry
School of Physics, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University（中山大学磁电物理与器件广东省重点实验室）
Exploring nontrivial topology at quantum criticality in a superconducting processor
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Zhejiang University（浙江大学物理学院、ZJU-杭州全球科创中心及浙江省微纳量子芯片与量子控制重点实验室）；Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学高等研究院及物理学院）
Topological Sector Fluctuations and Curie Law Crossover in Spin Ice
在低温下，自旋冰进入库仑相-一种具有代数相关性和拓扑约束自旋配置的状态。在Ho 2 Ti 2 O 7，我们已经观察到实验，这个过程是伴随着一个非标准的温度演变的波矢量依赖的磁化率，测量中子散射。分析和数值方法揭示了两个居里定律之间的交叉，一个表征高温顺磁制度，和其他的低温拓扑约束制度，我们称之为自旋液体居里定律的签名。该理论与中子散射实验结果吻合得很好。在更一般的基础上，i）两个居里定律的存在似乎是经典自旋液体的突现规范场的一般性质，ii）揭示了在阻挫材料中测量精确的居里-外斯温度的实验困难;（三）规范自由度和自旋自由度之间的映射意味着有限波矢处的磁化率可以用作波动的局部探针，拓扑扇区
