Surface and bulk critical phenomena in generalized quantum antiferromagnets

边界存在的临界现象是有趣物理的沃土，吸引了大量的实验和理论研究。在存在表面或更一般的边界的情况下，重整化组预测，控制整体临界行为的每个普适性类将分裂成不同的表面普适性类，从而产生丰富的相图。边界临界现象最近受到新的关注，原因是共形场理论的进步、从拓扑现象中获得的见解以及在前一个授权期内所取得的结果。在此基础上，我们建议通过蒙特卡罗模拟继续研究三维O(N)普适性类中的表面临界现象。一个相关的研究方向涉及嵌入到临界三维体中的对称破缺线缺陷的研究，其中在伊辛情况(N=1)中，我们先前已经证明了与该缺陷相关的唯一临界指数的出现。最后，在第三条线的研究中，也是受到正在进行的原子扫描隧道显微镜实验的启发，我们建议研究与二维量子自旋模型耦合的量子自旋链的临界行为，并调谐到其临界点。

Critical phenomena in the presence of boundaries is a fertile source of interesting physics, which has attracted numerous experimental and theoretical investigations. In the presence of surfaces or, more generally, boundaries, the Renormalization Group predicts that each universality class controlling the bulk critical behavior splits into different surface universality classes, leading to a rich phase diagram. Boundary critical phenomena has recently received a renewed attention, driven by advances in conformal field theory, insights from topological phenomena, as well as results obtained in the previous granting period. Building on these developments, we propose here to continue the investigation of surface critical phenomena in the three-dimensional O(N) universality class, by means of Monte Carlo simulations. A related direction of research concerns the investigation of a symmetry-breaking line defect embedded into a critical three-dimensional bulk, where in the Ising case (N=1) we have previously shown the emergence of a unique critical exponent associated to the defect. Finally, in a third line of research, motivated also by ongoing scanning tunneling microscopy experiments on adatoms, we propose to investigate the critical behavior of a quantum spin chain coupled to a two-dimensional quantum spin model, tuned to its critical point.