Quantum information scrambling in two-dimensional Bose-Hubbard lattices

It is a well-understood fact that the transport of excitations throughout a lattice is intimately governed by the underlying structures. Hence, it is only natural to recognize that the dispersion of information also has to depend on the lattice geometry. In the present work, we demonstrate that two-dimensional lattices described by the Bose-Hubbard model exhibit information scrambling for systems as little as two hexagons. However, we also find that the out-of-time-ordered correlator (OTOC) shows the exponential decay characteristic for quantum chaos only for a judicious choice of local observables. More generally, the OTOC is better described by Gaussian-exponential convolutions, which alludes to the close similarity of information scrambling and decoherence theory.