Structure of Measurement-Induced Entanglement in Infinite-Randomness Critical States

Abstract: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.

Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)

arXiv:2609.17670 [cond-mat.stat-mech]

(or arXiv:2609.17670v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2609.17670 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.