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arXiv · 2607.23871

Entanglement transitions and multifractality in monitored free-fermions with random long-range hopping

Bo Fan·Antonio M. García-García
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Abstract

We study the entanglement dynamics of a one-dimensional chain of monitored non-interacting complex fermions with random power-law hopping characterized by a decay exponent $\alpha$. For $\alpha \lesssim 1$, in stark contrast with the case of hopping to nearest neighbors, the scaling of the entanglement entropy (EE) of the steady state with system size $L$ is faster than logarithmic for any monitoring or disorder strength and it tends towards a linear (volume-law) scaling for sufficiently small $\alpha \lesssim 1/2$. For $\alpha > 3/2$, the EE is in the area-law phase, namely, no scaling with $L$, for any monitoring strength. For $1 < \alpha \lesssim 3/2$, we identify an $\alpha$-dependent measurement-induced phase transition (MIPT) at a critical value of the monitoring strength separating the mentioned area-law and sub-volume-law phases. At this critical point, the EE scales logarithmically with system size, and the density-density correlation function, closely related to the EE, exhibits multifractal features. These results highlight the importance of superdiffusive classical hopping in the entanglement dynamic of quantum many-body systems and also help differentiate its role with respect to conventional sources of entanglement such as genuine quantum non-locality.

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Bo Fan, Antonio M. García-García. 2026-07-26. Entanglement transitions and multifractality in monitored free-fermions with random long-range hopping. https://arxiv.org/abs/2607.23871

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