Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits
Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits
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DOI：
10.1103/physrevx.12.041002
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发表时间：
2021-07
影响因子：
12.5
通讯作者：
Utkarsh Agrawal;A. Zabalo;Kun Chen;Justin H. Wilson;A. Potter;J. Pixley;S. Gopalakrishnan;R. Vasseur
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作者：
Utkarsh Agrawal;A. Zabalo;Kun Chen;Justin H. Wilson;A. Potter;J. Pixley;S. Gopalakrishnan;R. Vasseur
纠缠的量子电路可以表现出纠缠跃迁作为测量速率的函数，这源于加扰幺正动力学和解纠缠投影测量之间的竞争。我们研究了如何在非幺正量子电路中的纠缠动力学可以丰富的电荷守恒的存在下，使用精确的数值和映射到一个统计力学模型的约束硬核随机游走器的组合。我们发现了一个电荷锐化的过渡，分离不同的混乱阶段与体积定律缩放纠缠，区分测量是否可以有效地揭示系统的总电荷。我们发现，虽然在没有测量的情况下，R 'enyi熵以亚弹道的方式增长，即使是最小的测量率，所有平均R' enyi熵都随着时间的推移而弹道地增长。我们数值研究了U（1）电路中电荷锐化和纠缠跃迁的临界行为，表明它们具有涌现的洛伦兹不变性，并且也可以用可扩展的局域辅助探针进行诊断。我们的统计力学映射技术很容易推广到任意阿贝尔群，和oebeers研究耗散稳定的拓扑破坏和拓扑秩序的一般框架。监控量子电路我们的数值计算结果表明，在纠缠（体积定律）状态下，在时间尺度t π p − 3 / 2上，p1]量子t到弹道量子t的标度有两个不同的阶段，然后（2）在交叉时间尺度t π L之后，电荷变尖锐，最后（3）系统在很长的时间尺度t π L上净化。
Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disen-tangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while R´enyi entropies grow sub-ballistically as √ t in the absence of measurement, for even an infinitesimal rate of measurements, all average R´enyi entropies grow ballistically with time ∼ t . We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively-stabilized symmetry-breaking and topological orders. monitored quantum circuits. Our numerical results indicate that there are two distinct phases in the entangling (volume-law) regime p 1 ] ∼ √ t to ballistic ∼ t scaling over a time scale ∼ p − 3 / 2 , then (2) charge sharpens after the crossover time scale t # ∼ L , and finally (3) the system purifies over a much long time scale t π ∼ e L .