Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics

Understand

Non-unitary evolution can give rise to novel steady states classified by their entanglement properties.

• In this work, we aim to understand its interplay with long-range hopping that decays with $r^{-\alpha}$ in free-fermion systems.
• We first study two solvable Brownian models with long-range non-unitary dynamics: a large-$N$ SYK$_2$ chain and a single-flavor fermion chain and we show that they share the same phase diagram.
• When $\alpha>0.5$, we observe two critical phases with subvolume entanglement scaling: (i) $\alpha>1.5$, a logarithmic phase with dynamical exponent $z=1$ and logarithmic subsystem entanglement, and (ii) $0.5<\alpha<1.5$, a fractal phase with $z=\frac{2\alpha-1}{2}$ and subsystem entanglement $S_A\propto L_A^{1-z}$, where $L_A$ is the length of the subsystem $A$.