周期边界条件的张量网络态算法以及其在费米Hubbard模型的应用

二维强关联的研究一直是凝聚态物理中具有挑战性的重要课题，数值方法在研究强关联问题中扮演着十分重要的角色。近来以纠缠投影态为代表的张量网络态算法，是被认为有望解决二维强关联系统的问题的方法。该方法已经成功的应用于各种强关联的自旋模型、玻色子模型和费米子模型。由于二维张量网络态有着较高的计算复杂度，该类算法只能应用于开放边界条件(OBC)，但不能应用于圆柱形边界条件(CBC)和周期边界条件(PBC)。本项目将研究张量网络态算法，提出可应用于CBC和PBC的张量网络态算法，并应用于费米Hubbard模型。

The numerical methods play an central role in solving the strongly correlated many-body systems which poses some of the most exciting open problems in physics. There is no such a method that is able to well simulate the physical system in two-dimensional case because of the failure of the perturbation theory. It is believe that the tensor network states(TNS) may be the key to the problem of simulation on the strongly correlated many-body systems. The TNS is widely used in various simulations such as spin models, boson models and the fermi models, and the method has obtain a great success. However the method is only access to the open boundary condition(OBC), and not to the cylindrical boundary condition(CBC) nor periodic boundary condition(PBC). In this program, we are going to improve the algorithms of TNS to get access to both the CBC and the PBC system and then apply it to the fermi-Hubbard model.