PIF2025 - Topology and strong interactions in non-equilibrium quantum simulators - (PID2024-159152NB-I00)

Quantum simulators, such as superconducting circuits or trapped ions, enable the creation of new phases of quantum matter. These new phases are important from a fundamental viewpoint, as they challenge our understanding of quantum complex systems. They can also find applications for designing precise sensors and amplifiers. In recent years, our group has developed a novel formalism for describing topological non-equilibrium phases of matter in quantum simulators. However, many questions remain open, like the role of interactions and disorder. This project will develop a theoretical description of complex topological phases based on analytical approaches and numerical algorithms. We will analyse how interactions lead to exotic new topological phases and explore their dynamical and structural properties.