测量改变的临界性理论
Theory of Measurement-Altered Criticality
AI总结：
该研究提出弱监测Tomonaga-Luttinger液体的测量改变临界性理论，通过复制瞬子计算等方法揭示测量诱导的关联特性，用矩阵乘积态计算验证结果，为1+1维共形场论基态的临界性提供新描述。
AI中文摘要：
局域测量可改变无隙量子物质中的长程关联。我们提出弱监测Tomonaga-Luttinger液体的理论，这是一类广泛存在的一维量子临界态。为解决测量记录的固有随机性，我们发展了复制瞬子计算方法，以研究玻恩平均可观测量。我们发现，当测量具有相关性时，密度和相位涨落的平均关联函数在长距离处按带对数修正的普适幂律衰减，我们认为这一特征是测量诱导随机性所特有的。我们表征了关联函数矩的全多分形谱，揭示了测量后态系综中存在广泛且强非高斯的涨落。我们用矩阵乘积态计算支持这些解析结果，并为1+1维共形场论描述的基态提供了测量改变临界性的整体图景。我们的结果表明，物理测量以一种既超出强制测量又超出常规临界标度的方式改变临界量子态。
英文摘要：
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.
