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

Abstract

Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand the effect of long-range hopping that decays with r-α in non-Hermitian free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-N SYK2 chain and a single-flavor fermion chain, and we show that they share the same phase diagram. When α > 0:5, we observe two critical phases with subvolume entanglement scaling: (i) α > 1:5, a logarithmic phase with dynamical exponent z = 1 and logarithmic subsystem entanglement, and (ii) 0:5 < α < 1:5, a fractal phase with z = 2α-1 2 and subsystem entanglement SA ⋊ L1-z A , where LA is the length of the subsystem A. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as L=T. We then confirm that the results are also valid for the static SYK2 chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurementinduced phase transitions.