Phase transitions beyond the Landau-Ginzburg-Wilson paradigm.

在朗道-金兹伯格-威尔逊的相变理论中，物质的状态是由一个局部序参量表征的，这个局部序参量一般与相的对称性破缺有关：超导性是一个复数，磁性是一个矢量。物质的许多相都逃脱了这种分类，并且处于固态，拓扑学和量子信息之间的研究前沿。它们包括对称性保护的拓扑相，例如以拓扑不变量为特征的拓扑绝缘体。拓扑有序相，如某些量子自旋液体，表现出几何依赖的基态简并，因此不能描述的局部序参数。这些相位只能通过使用纠缠测量来检测，并且由对面积定律的子引导校正唯一地定义。最后，Kondo销毁阶段仍然具有挑战性，以独特的特点。在这里，唯一可能的途径是使用量子信息技术的基础上的概念，近藤销毁和重费米子阶段表现出不同的纠缠特性之间的本地化和巡回自由度。 在这个项目部分，我们将使用状态近似自由量子蒙特卡罗方法来解决以下问题。(A)从纠缠的角度来看，近藤毁灭跃迁的独特特征是什么？ （B） 我们能否在广义Kitaev模型的热力学性质的数值计算和 Kitaev材料，如RuCl 3？(C)我们能提供实验上可实现的协议来测量相关材料中的纠缠吗？

In the Landau-Ginzburg-Wilson theory of phases and phase transitions, a state of matter is characterized by a local order parameter that is generically tied to the symmetry breaking properties of the phase: a complex number for superconductivity, a vector for magnetism. There are many phases of matter that escape this classification and that are at the forefront of research at the interface between the solid state, topology, and quantum information. They include symmetry protected topological phases such as topological insulators that are characterized by a topological invariant. Topologically ordered phases such as certain quantum spin liquids, exhibit geometry-dependent ground state degeneracy and hence cannot be described by a local order parameter. These phases can be detected only by using entanglement measures, and are uniquely defined by a sub-leading correction to the area law. Finally Kondo destruction phases remain challenging to characterize uniquely. Here, the only possible route is to use quantum information techniques based on the notion that Kondo destruction and heavy fermion phases exhibits different entanglement properties between the localized and itinerant degrees of freedom. In this project part, we will use state approximation free quantum Monte Carlo methods to address the following questions. (A) What are the unique signatures of the Kondo destruction transition from the perspective of entanglement? (B) Can we achieve a synergy between numerical calculations of thermodynamic properties of generalized Kitaev models and Kitaev materials such as RuCl3 ? (C) Can we provide experimentally realizable protocols to measure entanglement in correlated materials?