论文标题
测量引起的临界和纠缠簇：对1D和2D Clifford电路的研究
Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits
论文作者
论文摘要
量子动力学中的纠缠过渡呈现出非平衡系统中的一类新型相变。当多体量子系统经历统一的演化与受到监视的随机测量值散布时，稳态可以在体积和区域法之间表现出相变。在$ d $空间维度中，在非自动量子电路中测量引起的过渡与$ d+1 $尺寸的经典统计机械模型之间存在对应关系。在某些限制下，这些模型将其映射到渗透，但是有分析和数值证据表明，从这些限制中摆脱通用性类别应该通常与渗透不同。有趣的是，尽管有这些论点，但1D Qubit电路上的数字会产生散装指数，但仍接近2D渗透的指数，表面行为可能存在差异。在这项工作的第一部分中，我们研究了2D Clifford电路的关键特性。在大量中，我们发现了渗透图表所建议的许多属性，包括匹配的批量指数，以及关键纠缠增长的倒数幂律，$ s（t，l）\ sim l（1- a/t）$，饱和到区域法律。然后，我们利用基于图形状态的算法在1D和2D中分析稳定态纠缠簇的临界特性。我们表明，在具有简单的几何图渗透的模型中，投射横向场iSing模型，纠缠簇由渗透表面指数控制。但是，在Clifford模型中，我们发现群集指数与表面渗透的偏差很大，突出了任何可能的几何图对渗透的分解。鉴于偏离渗透普遍性类别的证据，我们的结果提出了一个问题，为什么许多批量特性与渗透相似。
Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with monitored random measurements, the steady-state can exhibit a phase transition between volume and area-law entanglement. There is a correspondence between measurement-induced transitions in non-unitary quantum circuits in $d$ spatial dimensions and classical statistical mechanical models in $d+1$ dimensions. In certain limits these models map to percolation, but there is analytical and numerical evidence to suggest that away from these limits the universality class should generically be distinct from percolation. Intriguingly, despite these arguments, numerics on 1D qubit circuits give bulk exponents which are nonetheless close to those of 2D percolation, with possible differences in surface behavior. In the first part of this work we study the critical properties of 2D Clifford circuits. In the bulk, we find many properties suggested by the percolation picture, including matching bulk exponents, and an inverse power-law for the critical entanglement growth, $S(t,L) \sim L(1 - a/t)$, which saturates to an area-law. We then utilize a graph-state based algorithm to analyze in 1D and 2D the critical properties of entanglement clusters in the steady state. We show that in a model with a simple geometric map to percolation, the projective transverse field Ising model, the entanglement clusters are governed by percolation surface exponents. However, in the Clifford models we find large deviations in the cluster exponents from those of surface percolation, highlighting the breakdown of any possible geometric map to percolation. Given the evidence for deviations from the percolation universality class, our results raise the question of why nonetheless many bulk properties behave similarly to percolation.
