AI 中文总结
本文通过有限尺寸RG交叉分析，研究弱测量下一维临界与三临界伊辛模型基态的测量后系综，揭示了两类模型中测量诱导的不同普适不动点及RG流结构。
AI 中文摘要
我们研究了三临界和一维量子伊辛哈密顿量基态的测量后系综，这两类基态分别受到弱能量测量和自旋测量，且未经过后选择。这些测量作为相关微扰作用于未被测量的临界基态。利用有限尺寸重整化群（RG）交叉分析，我们通过纠缠有效中心电荷、有效Affleck-Ludwig边界熵以及测量平均关联函数矩的多重分形特征来表征其普适性质。在两种情形下，我们均发现由固有玻恩法则随机性主导的“测量主导”或“测量改变”不动点的证据。对于临界伊辛模型，我们发现其存在流向投影测量不动点的直接RG流，该不动点满足面积定律纠缠；而对于三临界伊辛模型，我们发现其存在具有对数纠缠的弱测量不动点的证据。这些结果阐明了弱测量多临界伊辛基态的RG流结构，表明固有测量诱导的随机性如何在测量后系综中产生复杂且丰富的普适长程标度行为，且该行为可通过可控解析RG和数值有限尺寸RG交叉分析获取。
英文摘要
We study post-measurement ensembles of ground states of tricritical and critical 1D quantum Ising Hamiltonians subjected, respectively, to weak energy and spin measurements without post-selection. These measurements act as relevant perturbations about the unmeasured critical ground states. Using finite-size renormalization group (RG) crossover analyses, we characterize their universal properties through the entanglement effective central charge, effective Affleck-Ludwig boundary entropy, and signatures of multifractality from moments of measurement-averaged correlation functions. In both cases, we find evidence for "measurement-dominated" or "measurement-altered" fixed points governed by the underlying Born-rule randomness. For critical Ising, we find a direct RG flow to a projective-measurement fixed point with area-law entanglement, whereas for the tricritical Ising model, we find evidence for a weak-measurement fixed point with logarithmic entanglement. These results clarify the RG-flow structure of weakly measured multicritical Ising ground states and show how intrinsic measurement-induced randomness can generate complex and rich universal long-distance scaling behavior in the post-measurement ensembles, accessible to controlled analytical RG and numerical finite-size RG crossover analyses.
Comments16 pages, 8 figures, 2 tables
