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We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of integrability of Hamiltonians; TMI can be negative or positive for both integrable and non-integrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by non-integrability. Furthermore, we calculate TMI in disordered systems such as many-body localized (MBL) systems and the Sachdev-Ye-Kitaev (SYK) model. We find that scrambling occurs but is slow in a MBL phase, while disorder in the SYK model does not make scrambling slower but makes it smoother.
We show that the onset of quantum chaos at infinite temperature in two many-body 1D lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marke
We provide a protocol to measure out-of-time-order correlation functions. These correlation functions are of theoretical interest for diagnosing the scrambling of quantum information in black holes and strongly interacting quantum systems generally.
Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the lowest order co
We present a semiclassical treatment of one-dimensional many-body quantum systems in equilibrium, where quantum corrections to the classical field approximation are systematically included by a renormalization of the classical field parameters. Our s
Quantum chaotic interacting $N$-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales $sim!log N$. Here we show that, near criticality, certain many-body systems exhibit fast init