Measurement-induced L\'evy flights of quantum information

TL;DR

This paper investigates how frustrated local measurements in a one-dimensional free fermion system induce complex entanglement dynamics, including superdiffusive Le9vy flights, with a detailed theoretical model and numerical validation.

Contribution

It introduces a novel model of measurement-induced Le9vy flights in quantum entanglement, revealing fractal-scaling entropy and multiple dynamical regimes.

Findings

Superdiffusive entanglement growth with Sa0d7; a0rac{1}{3} a0scaling

Derivation of a non-linear sigma model with long-range couplings

Confirmation of Le9vy flights through large-scale simulations

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.