Phase transitions beyond the Landau-Ginzburg-Wilson paradigm.

在Landau-Ginzburg-Wilson的相变和相变理论中，物质的状态是由一个局域序参数来表征的，该参数一般与相的对称破缺性质有关：超导的复数，磁性的矢量。有许多阶段的物质逃脱了这个分类，并处于固态、拓扑和量子信息之间的界面研究的前沿。它们包括对称保护的拓扑相，例如由拓扑不变量表征的拓扑绝缘体。拓扑有序相，如某些量子自旋液体，表现出几何相关的基态简并，因此不能用局域有序参数来描述。这些相位只能通过使用纠缠测量来检测，并且通过对面积定律的次导修正来唯一地定义。最后，近藤销毁阶段仍然具有挑战性，难以独树一帜。这里，唯一可能的途径是使用量子信息技术，基于近藤破坏和重费米子相在定域自由度和巡回自由度之间表现出不同的纠缠特性的概念。在本项目部分，我们将使用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，近藤销毁过渡的独特特征是什么？(B)我们能否在广义Kitaev模型和诸如RuCl3等Kitaev材料的热力学性质的数值计算之间实现协同？(C)我们能否提供实验上可实现的协议来测量相关材料中的纠缠？

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?