We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.

We discuss thermofield double QFT at real time, in the large N limit. First, we establish a (dynamical) symmetry, which we argue holds in general for the real-time portion of the Schwinger–Kelydish contour. At large N, this symmetry is seen to generate a one-parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on an example of the $O\left(N\right)$ vector QFT. As a nontrivial application, we describe the construction of the corresponding (large N) thermofield double state in real-time collective formalism.

We discuss the large N expansion in backgrounds of extended states with a focus on the implementation of Goldstone symmetries and the construction of the associated Hilbert space. The formulation is given in the general framework of collective field theory. The case of translational symmetry is described first as a basic example. The large N thermofield represents the main topics, with the emergent dynamics of left–right bulk fields and collective symmetry coordinates. These give the basis for a $1/N$ expansion.

We develop analytical and numerical methods for the matrix thermofield in the large N limit. Through the double collective representation on the Schwinger-Keldysh contour, it provides thermodynamical properties and finite temperature correlation functions, for large N matrix quantum systems.

We discus Thermofield Double QFT at real time, in the large $N$ limit. First, we establish a (dynamical) symmetry which we argue holds in general on the real time portion of the Schwinger-Kelydish contour. At large $N$ this symmetry is seen to generate a one parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on the example of $O(N)$ vector QFT. As a nontrivial application we describe construction of the corresponding (large $N$) Thermofield Double State in real time collective formalism.

We discuss the large $N$ expansion in backgrounds of extended states with focus on implementation of Goldstone symmetries and the construction of the associated Hilbert space. The formulation is given in the general framework of collective field theory. Case of translational symmetry is described first, as the basic example. The large $N$ thermofield represents the main topics, with the emergent dynamics of Left-Right bulk fields and collective symmetry coordinates. These give the basis for a $1/N$ expansion.