Laboratoire de Physique Théorique
Toulouse - UMR 5152

In the study of quantum many-body systems, symmetries play a crucial role in understanding emergent phenomena and reducing computational complexity. Here I will explore how exploiting symmetries within the tensor network formalism can provide more insights into the properties of these complex systems. We will discuss how tensor networks serve as powerful tools for efficiently representing and simulating quantum states. By incorporating global symmetries in a local manner into these frameworks, we can significantly enhance the efficiency of numerical algorithms and capture essential features of quantum phases and transitions. The goal is to briefly introduce how tensor networks serve as numerical tools to study condensed matter systems, and then shed some light on the additional steps required to include symmetries, hinting at the underlying mathematical structures.