Data for "Theory of Measurement-Altered Criticality"

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. Numerical Data The data archive contains the numerical results used to support the matrix-product-state calculations presented in the referenced work. The calculations concern a one-third-filled interacting spin chain subjected to weak local density measurements. ground_state/ : DMRG ground states for L = 84,120, U1 =10, and U2 = 1.0,2.5. usual_corr_xjxk_weakmeasurez_born_final/: measurement-averaged connected correlation functions of X evaluated after sampling weak-measurement of outcomes of operator Z according to their Born probabilities. usual_corr_zjzk_weakmeasurez_born_final/: measurement-averaged connected correlation functions of Z evaluated after sampling weak-measurement of outcomes of operator Z according to their Born probabilities. usual_corr_zjzk_weakmeasurez_forced/: connected Z correlation functions obtained after post-selecting to the period 3 charge-density-wave measurement outcome. The files include the spatial separations, correlation values, measurement strengths, sample counts, and relevant simulation metadata. Data are provided in JLD2 and plain-text formats and are organized by system parameters and measurement protocol. Code The code archive contains Julia scripts used to generate the ground states, validate their critical properties, and calculate the post-measurement correlation functions: gs.jl — generates one-third-filled interacting spin-chain ground states using DMRG. gs_verification.jl — evaluates entanglement entropy and correlation functions used to verify criticality and extract the Luttinger parameter. usual_corr_zjzk_weakmeasurez_born.jl — samples weak density-measurement outcomes from the Born distribution and computes connected density correlators. usual_corr_xjxk_weakmeasurez_born.jl — performs the same Born-sampled measurement protocol and computes connected transverse correlators. usual_corr_zjzk_weakmeasurez_forced.jl — computes connected density correlators for the CDW outcome. The archive also includes README.md with usage instructions and the Julia environment files Project.toml and Manifest.toml. The environment was generated with Julia 1.12.4; the manifest records the exact resolved package versions used for the calculations.