Unveiling 2D Correlated Topological Insulators through Tensor Network States

In strongly correlated systems, the traditional concept of electronic bands becomes inadequate, limiting its utility in studying topological insulators within the correlated regime. Although exactly solvable models can be constructed, the formulation of generic variational wavefunctions for numerical simulations is highly desirable. In this work, we tackle this challenge by developing a comprehensive framework for fermionic tensor network states. Starting from simple assumptions, we derive sets of tensor equations for any given symmetry group, capturing consistent relations that govern symmetry transformation rules on tensor legs. By applying the solutions of these equations to local tensors, we obtain generic variational wavefunctions that correspond to various topological insulator phases. Additionally, we present numerical results using variational wavefunctions, including calculations of the many-body topological invariant and evaluations of the disorder operator.