Information spreading in many-body systems and the out-of-time-ordered correlator

The information spreading in quantum many-body systems under unitary real-time evolution is related to the growth of simple Heisenberg operators, which is quantified by out-of-time-order correlation (OTOC) functions. Using a time-dependent disordered Hamiltonian model, I will analytically show the emergence of hydrodynamics description of the OTOC arising from the unitary real-time dynamics. Corrections of quantum fluctuation are manifested as the diffusively broadened wavefront of the OTOC. This picture is supported by large-scale (~200 spins) real-time dynamics simulation on realistic spin Hamiltonians using our newly developed tensor-network method.