Seminarium Fizyki Materii Skondensowanej

In this general talk, I will introduce some of the key challenges that numerical approaches face when applied to model Hamiltonian systems, including issues of scaling, convergence, and stability. I will then outline a sequence of recent advancements—ranging from analytic interpolation techniques to tensor-network-based contraction strategies—that are paving the way for the next generation of computational tools in materials physics and chemistry. Finally, I will highlight concrete examples of applications, illustrating how these methods can provide new insights into correlated electron models and molecular systems, and pointing toward future directions where such tools may enable meaningful discovery.