论文标题
随机树张量网络中的平均场纠缠过渡
Mean-field entanglement transitions in random tree tensor networks
论文作者
论文摘要
量子混沌系统中的纠缠相变和随机张量网络中的纠缠相变已成为一类新的关键点，将各个阶段分开具有不同的纠缠缩放。我们通过研究随机树张量网络的纠缠特性提出了这种过渡的平均场理论。作为键尺寸的函数，我们发现一个相变的区域law与纠缠熵的对数尺度分开。使用在Cayley树和空腔方法上定义的复制统计力学模型上的映射，我们分析了此类过渡的缩放属性。我们的方法提供了纠缠过渡的典型，均值的示例。我们通过直接计算随机树张量网络状态的纠缠来验证我们的预测。
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.
