费米子张量网络中的强关联拓扑物态

强关联电子体系是探索搜寻各种拓扑量子物态的温床。这类物态不仅仅在科学上非常吸引人，同时也具有潜在的应用价值：它们也许可以被用来制造新型量子器件甚至是量子计算机。..然而，在强关联系统中，传统的能带理论不再管用，第一性计算方法往往不能给出可靠的预言。因此，为了在这类体系中寻找拓扑量子物态，研究者有必要去发展新的理论和数值方法。..在此项目中，申请人将着重考虑费米子张量网络。张量网络起源于量子信息领域，并很快在凝聚态和高能领域中得到广泛应用。它天然适用于描述量子系统中复杂的纠缠结构，而且配套有强大的数值方法。因此，它成为了强关联体系中变分计算的强有力工具。现有研究往往集中于玻色子张量网络，而相对缺乏关于费米子张量网络的研究工作。有鉴于此，申请者将致力于费米子张量网络上的拓扑物态的研究，包括发展这类物态的张量网络表示，并开发相应的数值模拟算法。

Strong correlations in electronic systems may lead to many exotic quantum phases, including topological phases such as fractional quantum Hall phases. These phases not only are scientifically attractive, but also serve as possible candidates to build novel quantum devices and quantum computers. ..However, in correlated systems, traditional band theory is no longer a good starting point, and numerical methods based on First principle calculation fail to give reliable prediction. Thus, it is highly desirable to develop new theoretical and numerical tools for physicists to search for topological phases in such systems...In this proposal, we try to develop methods based on fermionic tensor networks. Tensor networks are first introduced in quantum information community, and soon become popular in other fields such as condensed matter and high energy. Tensor networks are the most natural language to describe complicated quantum entanglement structure. Besides, numerical algorithm based on tensor networks are very powerful. Thus, they are great tools to perform variational calculation for topological phases in strongly correlated systems. However, comparing to bosonic tensor networks, there are very few works on fermionic ones. Here, we hope to develop general framework on fermionic tensor networks to classify topological phases, to develop efficient numerical algorithms, and finally to apply to realistic electronic models.