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This research investigates how continuous weak measurements fundamentally alter the critical behavior of one-dimensional quantum systems, introducing unique power-law decay patterns driven by measurement-induced randomness rather than conventional scaling. By combining replica instanton calculations with matrix-product-state simulations, the study reveals a distinct multifractal spectrum that characterizes post-measurement states in gapless matter. These findings advance our theoretical understanding of how observation protocols reshape long-range correlations in quantum critical regimes beyond standard forced measurements.
Theory of Measurement-Altered Criticality
arXiv:2608.05289v1 Announce Type: cross 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.
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.
Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2608.05289 [cond-mat.stat-mech]
(or arXiv:2608.05289v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2608.05289 arXiv-issued DOI via DataCite (pending registration)
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