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We model backreaction in AdS$_2$ JT gravity via a proposed boundary dualSachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it fromthe perspective of quantum entanglement and chaos. The boundary effectiveaction accounts for the backreaction through a linear coupling of the Diracfermions to the Gaussian-random two-body Majorana interaction term in thelow-energy limit. We calculate the time evolution of the entanglement entropybetween graviton and Dirac fermion fields for a separable initial state andfind that it initially increases and then saturates to a finite value.Moreover, in the limit of a large number of fermions, we find a maximallyentangled state between the Majorana and Dirac fields in the saturation region,implying a transition of the von Neumann algebra of observables from type I totype II. This transition in turn indicates a loss of information in theholographically dual emergent spacetime. We corroborate these observations witha detailed numerical computation of the averaged nearest-neighbor gap ratio ofthe boundary spectrum and provide a useful complement to quantum entanglementstudies of holography.

On the Backreaction of Dirac Matter in JT Gravity and SYK Model