Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions
Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions
复制标题
测量引起的转变时的算子缩放维度和多重分形
DOI：
10.1103/physrevlett.128.050602
复制
发表时间：
2022
影响因子：
8.6
通讯作者：
Pixley, J. H.
中科院分区：
文献类型：
--
作者：
Zabalo, A.;Gullans, M. J.;Wilson, J. H.;Vasseur, R.;Ludwig, A. W. W.;Gopalakrishnan, S.;Huse, David A.;Pixley, J. H.
量子多体系统的局域重复测量可以引起纠缠结构的相变。这些由测量引起的相变(MIPT)已经被研究用于各种类型的动力学，然而大多数情况下产生的临界指数在数量上相似，这使得人们不清楚存在多少不同的普适性类别。在这里，我们用数值传递矩阵方法研究了控制这些MIPT的共形场论的性质，它允许我们提取有效的中心电荷，以及()维系统在这些临界点上算符的最初几个低位标度维。我们的结果提供了令人信服的证据，证明了量子比特的一般MIPT和Clifford MIPT属于不同的普适类，并且在大的在位Hilbert空间维度的极限下，它们都不同于量子比特的渗流跃迁。对于一般情况，我们发现了关联函数在临界点的多重分形标度的有力证据，这反映在标度维的连续谱上。
Repeated local measurements of quantum many-body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar critical exponents, making it unclear how many distinct universality classes are present. Here, we probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points for ()-dimensional systems. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large on-site Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.