摘要 (Abstract) ：

In this talk, I will present our study of high-temperature cuprate superconductors using the fermionic tensor network method—an advanced entanglement-based numerical approach capable of overcoming the notorious sign problem. By revisiting the standard t-J model, we surprisingly find that its ground-state manifold hosts a richer variety of superconducting states than previously expected. In addition to the conventional d-wave pairing, we identify various pairing density wave states as well as a fragile s-wave state. Our results suggest that pairing and global phase coherence may emerge separately in high-temperature superconductors. Finally, I will discuss possible pairing and superconducting mechanisms driven by geometric phase frustrations in these systems.