Unitary and dissipative chaos in a canonical bosonic analog of the SYK model

The Sachdev-Ye-Kitaev (SYK) model of N all-to-all randomly coupled Majorana fermions exhibits quantum chaos, is exactly solvable in the large N limit, and possesses a holographic gravity dual. It has thus been of much interest to both the high energy physics and condensed matter physics communities in recent years. While it is natural to ask whether a canonical bosonic analog would share these properties, simplest constructions often lead to instabilities, non-SYK behavior, or analytically intractable systems. Some alterations like adding a large mass term, using hard-core bosons instead, and a recent approach using Fock space fluxes have been suggested to address these challenges. In this talk, we present an alternative approach, constructing a system of N canonical bosons with all-to-all interactions defined through quadratic forms of M Gaussian random terms. One advantage of this approach is that it is analytically tractable in the large N and M limits with standard mean-field techniques, leading to an effective action like the fermionic SYK one. Another advantage is that it can be easily generalized to include dissipation by adding similar interactions in the Lindbladian instead. We calculate various indicators of quantum chaos including eigenvalue spacing ratios, out-of-time-order correlators (OTOCs), and logarithmic OTOCs, in both the unitary and dissipative cases, and discuss whether the system is quantum-chaotic. Lastly, we discuss the implications for a holographic gravity dual in each case.