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arXiv · 2608.05289

Theory of Measurement-Altered Criticality

Kabir Khanna·Sara Murciano·Romain Vasseur
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Abstract

Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevant, average correlators of density and phase fluctuations decay at long distances as universal power laws with logarithmic corrections, a feature we argue is peculiar to measurement-induced randomness. We characterize the full multifractal spectrum of moments of correlations functions, revealing broad, strongly non-gaussian fluctuations across the ensemble of post-measurement states. We support these analytic results with matrix-product-state calculations, and provide a general picture of measurement-altered criticality for ground states described by 1+1d conformal field theories. Our results establish that physical measurements alter critical quantum states in a manner that lies beyond both forced measurements and conventional critical scaling.

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Kabir Khanna, Sara Murciano, Romain Vasseur. 2026-08-05. Theory of Measurement-Altered Criticality. https://arxiv.org/abs/2608.05289

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