CMSA Topological Quantum Matter Seminar: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States

The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has been established that topological insulator phases persist as stable phases. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wavefunctions for numerical simulations is highly desirable.
In this talk, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions, we write down tensor equations, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems.