Stability of quantum symmetries against perturbations

Symmetries play a fundamental role in describing quantum systems. They are represented by the operators that stay constant over time, which happens when they commute with the Hamiltonian of the system. However, when the Hamiltonian is slightly perturbed, not all symmetries behave the same way. Some remain nearly conserved throughout the evolution: these are called robust symmetries. Others, instead, drift significantly from their original values for sufficiently long times: these are known as fragile symmetries. Our goal is to provide a precise characterization of both robust and fragile symmetries.