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Range-Controlled Entanglement in Lindbladian Skin States of Monitored Fermions
Understanding how measurements and dissipation shape many-body entanglement is a central question in quantum information dynamics. I will discuss a monitored fermionic chain where directed particle-conserving dissipation competes with coherent hopping of tunable range. The dissipative dynamics generates a Lindbladian skin effect: particles are driven toward one boundary, but Pauli exclusion converts edge accumulation into a many-body density imbalance rather than macroscopic occupation of a single mode.
By unraveling the Lindblad dynamics into quantum-jump trajectories, we characterize the monitored steady-state ensemble through two complementary diagnostics: the density imbalance, which detects skin accumulation, and the half-chain entanglement entropy, which probes its quantum-information structure. We find that the range of coherent hopping acts as a control knob for entanglement scaling. Short-range hopping yields complete skin accumulation and area-law entanglement. In contrast, sufficiently long-range hopping destabilizes the complete Fermi skin, leaving a finite density tail in the bulk and producing algebraic sub-volume entanglement growth.
A scaling argument explains this crossover: long-range hopping maintains a finite coherent coupling between the skin domain and an extensive part of the chain, whereas this coupling vanishes in the short-range regime. Thus, directed dissipation and coherent drive jointly control not only particle localization, but also the organization of quantum correlations in monitored many-body states. These results provide a route toward reservoir-engineering entanglement structures beyond conventional unitary dynamics.
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