Charge transport and chaos in the complex Brownian SYK chain

Extended chaotic quantum systems with global symmetries allow for transport of localized charges and display quantum information scrambling, both of which depend on the nature of interactions in the system. The properties of transport and scrambling are therefore implicitly related, and to study the interplay between the two, we utilize the Complex Brownian SYK model defined on a one-dimensional lattice. We investigate the charge-transport through the two-point correlator of charge density in both the free (quadratic inter-site couplings) and interacting (quartic inter-site couplings) model, which post-disorder averaging maps to the imaginary time dynamics of an effective spin-chain with an SU(2) x U(1) symmetry. The quantum information scrambling is probed via the out-of-time-ordered correlator, the computation of which is also mapped to an effective spin chain that evolves in imaginary time and displays an SU(4) x U(1) symmetry. This mapping to spin models with SU(n) symmetries enables us to analytically solve the free model and numerically investigate the interacting model for large system size using tensor network techniques, which we then utilize to outline the relation between charge transport and scrambling in the Complex Brownian SYK chain.