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 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 $A$. 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 SYK${}_2$ 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.

17 pages, 5 figures

References in corpus (19)

• Critical properties of the measurement-induced transition in random quantum circuits
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Fate of measurement-induced phase transition in long-range interactions
• Symmetry enriched phases of quantum circuits
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Spacetime duality between localization transitions and measurement-induced transitions
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
• The Lieb-Robinson light cone for power-law interactions
• Dispersive SYK model: band structure and quantum chaos
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Chiral Topological Superconductors Enhanced by Long-Range Interactions
• Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Note on entropy dynamics in the Brownian SYK model

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