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arXiv · 2501.12903

Measurement-induced L\'evy flights of quantum information

Igor Poboiko·Marcin Szyniszewski·Christopher J. Turner·Igor V. Gornyi·Alexander D. Mirlin·Arijeet Pal
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Abstract

We explore a model of free fermions in one dimension, subject to frustrated (non-commuting) local measurements across adjacent sites, which resolves the fermions into non-orthogonal orbitals, misaligned from the underlying lattice. For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate at one point in the Brillouin zone, which generates fractal-scaling entanglement entropy $S \propto \ell^{1/3}$ for a subsystem of length $\ell$. We derive an effective non-linear sigma model with long-range couplings responsible for L\'evy flights in entanglement propagation, which we confirm with large-scale numerical simulations. When the misalignment is reduced, the entanglement exhibits, with increasing $\ell$, consecutive regimes of superdiffusive, $S\propto \ell^{1/3}$, diffusive, $S\propto \ln \ell$, and localized, $S = \rm{const}$, behavior. Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians and measurements.

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Igor Poboiko, Marcin Szyniszewski, Christopher J. Turner, Igor V. Gornyi, Alexander D. Mirlin, Arijeet Pal. 2025-01-22. Measurement-induced L\'evy flights of quantum information. https://doi.org/10.1103/tx71-1cd9

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