Operator Algebraic Methods in Topological Phases and Quantum Information

当代凝聚态物理学的一个重大发现是存在着不符合朗道理论的物质相，而是“拓扑有序”的。在那里，某些性质取决于底层系统的拓扑性质。这使得它们成为建造量子计算机或存储器的有吸引力的候选者，特别是使用称为任意子的准粒子。还有许多有趣的数学联系：除了拓扑学，算子代数，表示论和模张量范畴也起着重要作用。在这个助学金的支持下，您将学习2D间隙拓扑相位的数学物理，并应用于量子信息理论，以找到涵盖所有已知示例的包容性理论。一个障碍是没有好的方法从底层系统中提取任意子的属性。您将使用算子代数技术开发工具，直接在热力学极限中完成此操作

A major discovery in contemporary condensed matter physics was the existence of phases of matter that do not fit in Landau's theory, but instead are "topologically ordered". There, certain properties depend on topological properties of the underlying system. This makes them attractive candidates to build a quantum computer or memory, in particular using quasi-particles called anyons. There are many interesting mathematical connections as well: besides topology, operator algebras, representation theory and modular tensor categories play an essential role. Supported by this studentship, you will study the mathematical physics of 2D gapped topological phases, with applications to quantum information theory, to find an encompassing theory that covers all known examples. A roadblock is that there is no good way to extract the properties of the anyons from the underlying system. You will use operator algebraic techniques to develop tools to do this directly in the thermodynamic limit