  We construct a series of one-dimensional non-unitary dynamics consisting of
both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model.
Starting from a short-range entangled state, we analyze the entanglement
dynamics using the path integral formalism in the large $N$ limit. Among all
the results that we obtain, two of them are particularly interesting: (1) By
varying the strength of the imaginary evolution, the interacting model exhibits
a first order phase transition from the highly entangled volume law phase to an
area law phase; (2) The one-dimensional free fermion model displays an
extensive critical regime with emergent two-dimensional conformal symmetry.
