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A main feature of a chaotic quantum system is a rigid spectrum where thelevels do not cross. We discuss how the presence of level repulsion in latticemany-body quantum systems can be detected from the analysis of their timeevolution instead of their energy spectra. This approach is advantageous toexperiments that deal with dynamics, but have limited or no direct access tospectroscopy. Dynamical manifestations of avoided crossings occur at longtimes. They correspond to a drop, referred to as correlation hole, below theasymptotic value of the survival probability and by a bulge above thesaturation point of the von Neumann entanglement entropy and the Shannoninformation entropy. In contrast, the evolution of these quantities at shortertimes reflect the level of delocalization of the initial state, but notnecessarily a rigid spectrum. The correlation hole is a general indicator ofthe integrable-chaos transition in disordered and clean models and as such canbe used to detect the transition to the many-body localized phase in disorderedinteracting systems.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge