How does classical chaos affect the generation of quantum
entanglement? What signatures of chaos exist at the quantum level and how
can they be quantified? These questions have puzzled physicists for a
couple of decades now. We answer these questions in spin systems by
analytically establishing a connection between entanglement generation and
a measure of delocalization of a quantum state in such systems. While
delocalization is a generic feature of quantum chaotic systems, it is more
nuanced in regular systems. We explore when the quantum dynamics mimics a
localized classical trajectory, and find criteria to quantify Bohr's
correspondence principle in periodically driven spin systems. These
criteria are typically violated in a deep quantum regime due to
delocalized evolution. Using our criteria, we establish that entanglement
is a signature of chaos only in a semiclassical regime. Our work provides
a new approach to analyzing quantum chaos and designing systems that can
efficiently generate entanglement.
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