无限随机临界态中测量诱导纠缠的结构
Structure of Measurement-Induced Entanglement in Infinite-Randomness Critical States
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中文总结 AI 辅助
针对无限随机临界态，提出测量理论，证明测量诱导纠缠以普适指数幂律衰减，且临界性质稳健，为无序临界态测量研究提供新平台。
中文摘要 AI 辅助
投影测量对多体量子态的影响与其底层纠缠结构紧密相关。临界态尤其敏感，因为长程纠缠使得局部测量能够产生全局后果。这一现象已在由共形场论（CFT）描述的临界态背景下得到广泛研究，其中测量可以改变后测量量中的临界性质（“测量改变临界性”），并诱导具有普适特征的纠缠（“测量诱导纠缠”）。相比之下，对于具有淬火无序、且无法用CFT描述的临界态，测量所起的作用知之甚少。在此，我们发展了一套针对由无限随机不动点（IRFPs）控制的一维临界态的测量理论，聚焦于两个紧密相关的例子：随机XXZ链和随机横场伊辛模型。我们证明，在这两个模型中，测量诱导纠缠以具有普适指数$(3-\sqrt{5})/2$的幂律衰减，并且建立该纠缠所需的最小测量次数服从普适标度形式。当仅进行有限密度的测量时，我们证明态的临界性质异常稳健：“测量改变临界性”不存在，测量要么保持临界指数不变，要么完全破坏临界性。这些结果确立了IRFPs作为临界态测量研究的一个可解析处理的平台，与CFT情形互补。在干净系统中需要复制方法的输出随机性在无限随机性下变得平凡，普适响应由淬火无序诱导的统计决定。
英文摘要
The impact of projective measurements on a many-body quantum state is tightly linked to its underlying entanglement structure. Critical states are particularly sensitive, as long-range entanglement allows local measurements to have global consequences. This has been extensively studied in the context of critical states described by a conformal field theory (CFT), where measurements can alter critical properties in post-measurement quantities ('measurement-altered criticality') and induce long-range entanglement with universal features ('measurement-induced entanglement'). By contrast, little is known about the role of measurements on critical states with quenched disorder, which admit no CFT description. Here, we develop a theory of measurements on one-dimensional critical states governed by infinite-randomness fixed points (IRFPs), focusing on two closely related examples: the random XXZ chain and the random transverse-field Ising model. We show that the measurement-induced entanglement decays as a power-law with universal exponent $(3-\sqrt{5})/2$ in both models, and that the minimum number of measurements required to establish this entanglement obeys a universal scaling form. When only a finite density of measurements is made, we show that the critical properties of the state are remarkably robust: `measurement-altered criticality' is absent, with measurements either preserving the critical exponents, or destroying the criticality entirely. These results establish IRFPs as an analytically tractable arena for measurements on critical states, complementary to the CFT case. The outcome randomness that necessitates replica methods in clean systems becomes trivial at infinite randomness, with the universal response governed by the statistics induced by the quenched disorder.
发表机构
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory（鲁道夫·皮尔斯理论物理中心，克拉伦登实验室）
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