Pure states in the SYK model and nearly-$AdS_2$ gravity

TL;DR

This paper studies pure states in the SYK model, showing their correlators resemble thermal ones, and explores their gravity duals in nearly-$AdS_2$ space, revealing insights into entanglement and horizon regions.

Contribution

It introduces a simple local condition for pure states in the SYK model, analyzes their correlators, and connects these states to nearly-$AdS_2$ gravity configurations with horizons.

Findings

Diagonal correlators match thermal correlators at large N.

Off-diagonal correlators decay over time, related to thermal correlators.

Subsystems become entangled after a certain interaction time.

Abstract

We consider pure states in the SYK model. These are given by a simple local condition on the Majorana fermions, evolved over an interval in Euclidean time to project on to low energy states. We find that "diagonal" correlators are exactly the same as thermal correlators at leading orders in the large $N$ expansion. We also describe "off diagonal" correlators that decay in time, and are given simply in terms of thermal correlators. We also solved the model numerically for low values of $N$ and noticed that subsystems become typically entangled after an interaction time. In addition, we identified configurations in two dimensional nearly-$AdS_2$ gravity with similar symmetries. These gravity configurations correspond to states with regions behind horizons. The region behind the horizon can be made accessible by modifying the Hamiltonian of the boundary theory using the the knowledge of the particular microstate. The set of microstates in the SYK theory with these properties generates the full Hilbert space.