Effect of symmetries in out-of-time ordered correlators in interacting integrable and nonintegrable many-body quantum systems

Out-of-time ordered correlators (OTOCs) help characterize the scrambling of quantum information and are usually studied in the context of nonintegrable systems. We compare the relaxation dynamics of OTOCs in interacting integrable and nonintegrable many-body quantum systems in the presence of U(1) symmetry and supersymmetry. We show that their dynamics exhibit similar behaviors, with a time dependence that is mostly determined by the symmetry rather than integrability, and they follow closely the dynamics of two-point correlators. We study the OTOCs dynamics using numerical calculations, and gain analytical insights from the properties of the diagonal and of the off-diagonal matrix elements of the OTOCs local operators in the energy eigenbasis.