Spread of entanglement in a Sachdev-Ye-Kitaev chain

We study the spread of Renyi entropy between two halves of a Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermo field double (TFD) state. The SYK chain model is a model of chaotic many-body systems, which describes a one-dimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer Renyi index n > 1, the Renyi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly-AdS 2 gravity.