Tensor Networks for Chiral Topological Order

本项目旨在利用纠缠和张量网络的工具发现物质拓扑相的新特性。具体来说，主要目标是开发一种算法，用于数值研究具有二维手性拓扑顺序的量子多体系统，这反过来又对应于具有拓扑性质的材料的最相关实验实现。数值方法将使用量子多体态的张量网络描述来实现，例如有限和无限投影纠缠对态（PEPS）。这种提出的计算方法从未在张量网络方法的背景下实现，并且将构成一个非常有用的工具，因为它将允许超出当前数值方法范围的计算。该方法将成为研究拓扑绝缘子和拓扑莫特绝缘子的天然工具，在许多相关情况下，主要缺乏可靠的数值方法。此外，作为张量网络描述的副产品，我们的方法也将允许研究这些系统的多体纠缠特性。这将使用量子信息工具，如纠缠谱、拓扑熵和拓扑几何纠缠来完成。对这些量的研究有望从微观自由度对二维手性拓扑量子物质出现的物理机制产生新的见解。

This project aims at finding novel properties of topological phases of matter using the tools of entanglement and tensor networks. Specifically, the main goal is to develop an algorithm for numerically studying quantum many-body systems with 2d chiral topological order, which in turn correspond to the most relevant experimental realizations of materials with topological properties. The numerical method will be implemented using tensor network descriptions of quantum many- body states, such as finite and infinite Projected Entangled Pair States (PEPS). This proposed computational approach has never been implemented in the context of tensor network methods, and will constitute a very useful tool since it will allow calculations beyond the reach of current numerical methods. The resulting method will be a natural tool to study topological insulators and topological Mott insulators, where in many relevant cases a reliable numerical method is mainly missing. Moreover, our methods will also allow to study, as a by-product of the tensor network description, the many-body entanglement properties of these systems. This will be done using quantum information tools such as entanglement spectrum, topological entropy and topological geometric entanglement. The investigation of these quantities is expected to produce new insights into the physical mechanisms underlying the emergence of chiral topological quantum matter in 2d from microscopic degrees of freedom.