测量诱导的量子信息莱维飞行
Measurement-induced Lévy flights of quantum information
AI总结：
本研究通过一维自由费米子模型，发现受挫局域测量可诱导量子信息超扩散传播，产生分形标度纠缠熵，并揭示错位程度调控超扩散、扩散与局域化转变的机制。
摘要：
我们探索了一维自由费米子模型，该模型受到跨相邻位点的受挫（非对易）局域测量的影响，这些测量将费米子分解为非正交轨道，与底层晶格错位。对于最大错位，超扩散行为源于布里渊区中一点处测量诱导的准粒子衰减率消失，这为长度为$\ell$的子系统的纠缠熵产生分形标度$S \propto \ell^{1/3}$。我们推导了一个具有长程耦合的有效非线性sigma模型，该模型负责纠缠传播中的莱维飞行，并通过大规模数值模拟加以确认。当错位减小时，随着$\ell$的增加，纠缠表现出连续的超扩散（$S\propto \ell^{1/3}$）、扩散（$S\propto \ln \ell$）和局域化（$S = \rm{const}$）行为区域。我们的发现表明，对于局域哈密顿量和测量，可以产生复杂的分形标度纠缠。
英文摘要：
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 Lévy 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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