Exponential decay of OTOC and Lyapunov exponent extraction in the Anderson-Hubbard model

Determine whether the out-of-time-order correlator of the Anderson-Hubbard model with random local disorder in the metallic, weak-coupling regime exhibits exponential decay in time, and accurately extract the corresponding Lyapunov exponent that characterizes the chaos and information scrambling in this system.

Background

The paper studies the out-of-time-order correlator (OTOC) in the Anderson-Hubbard model using a non-equilibrium DMFT framework combined with coherent potential approximation (CPA) and a second-order perturbative impurity solver on a double-folded Schwinger-Keldysh contour. The authors find that random local disorder accelerates the initial decay of the OTOC in the metallic phase for weak interactions.

Due to limitations in the available time window and the perturbative nature of the solver, the authors report that their current data do not allow them to conclusively establish an exponential decay of the OTOC or to accurately determine the associated Lyapunov exponent, leaving this characterization unresolved.