对称性破缺测量下测量诱导临界性的普适性
Universality of Measurement-Induced Criticality under Symmetry-Breaking Measurements
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中文总结 AI 辅助
研究具有\(U(1)\)对称性的随机量子电路在对称性破缺测量下的临界性质，发现其在测量诱导相变处有普适临界性，通过经典统计力学模型及数值分析，证明电荷关联长度有限，排除电荷锐化转变。
中文摘要 AI 辅助
我们研究了具有\(U(1)\)对称性的随机量子电路在局部投影测量下的临界性质，这些测量明确打破了这种对称性。我们发现，在测量诱导的相变处，对称性破缺测量在大尺度上起到相关微扰的作用，导致与具有非对称酉动力学的相应监测随机电路相同的普适临界性质。特别地，我们考虑在大局部希尔伯特空间维度极限下的监测\(U(1)\)对称哈尔随机电路，其中轨迹平均纠缠熵可以根据经典统计力学模型精确获得。在这个模型中，与守恒定律相关的电荷遵循对称简单排斥过程，其中对称性破缺测量对应于产生和破坏电荷的无序缺陷。我们证明，与对称性保持测量的情况相反，对于任何测量速率，电荷关联长度都保持有限，排除了电荷锐化转变。我们通过对监测\(U(1)\)对称哈尔和稳定器随机电路中纠缠转变的数值有限尺寸缩放分析，进一步支持了我们在有限局部希尔伯特空间维度下的预测。
英文摘要
We study the critical properties of random quantum circuits with a $U(1)$ symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored $U(1)$-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored $U(1)$-symmetric Haar and stabilizer random circuits.
