Quantum information scrambling in two-dimensional Bose-Hubbard lattices

Abstract

Despite initial and outspoken hesitation, quantum chaos has established itself as a veritable field of modern research. However, whereas classically chaotic dynamics describes the behavior of trajectories in phase space, quantum chaos refers to the exponentially fast dispersion of information throughout a quantum many-body system. Interestingly, quantum information scrambling originated in a resolution of the black-hole information paradox, in which it was recognized that any information crossing the event horizon is chaotically scrambled across the entire horizon. Yet, succinct analyses of the rate of quantum information scrambling require the solution of complex many-body dynamics. In the present analysis, we study such complex dynamics, namely, the Bose–Hubbard model on two-dimensional lattices. We find that already small lattices consisting of two hexagons exhibit evidence of chaotic behavior, but also that the geometry of the underlying lattice governs the overall behavior. Borrowing tools and ideas from decoherence theory we re-emphasize previous results suggesting that information scrambling and decoherence, i.e., loss of quantum information into an environment share many similarities.