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

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(-alpha) 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 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 = 2 alpha-1/2 and subsystem entanglement S-A proportional to L-A(1-z) , 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 measurement induced phase transitions.

Automated summary

The study investigates the impact of long-range hopping on non-Hermitian free-fermion systems, revealing the emergence of novel steady states characterized by their entanglement properties. Two critical phases are observed when α > 0.5, including a logarithmic phase and a fractal phase with distinct subsystem entanglement scaling.