Spread of entanglement and causality
Spread of entanglement and causality
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纠缠与因果关系的传播
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Mezei
中科院分区：
文献类型：
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作者：
H. Casini;Hong Liu;M. Mezei
本文研究了相对论理论中纠缠熵在整体猝灭后的时间演化的因果关系约束。我们首先提供了一个一般性的证明，即所谓的海啸速度是有界的光速。然后，我们将[1]的自由粒子流模型推广到一般的维数和任意的纠缠模式的初始状态。在两个以上的时空维度中，这些模型中纠缠的传播对初始纠缠模式高度敏感，但我们能够证明纠缠熵增长的归一化速率的上限，因此海啸速度。这个界限比全息理论中的猝灭要小，这突出了相互作用在多体系统中纠缠传播中的重要性。我们提出了一个相互作用的模型，我们相信提供了一个上限的相互作用相对论理论的纠缠传播。在具有多个间隔的两个时空维度中，这个模型及其变体能够再现全息理论在参数空间的重要部分所展示的复杂结果。对于更高的维度，该模型将海啸的速度限制在光速。最后，我们构建了一个几何模型的纠缠传播的基础上的张量网络结构的整体淬火。
A bstractWe investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then generalize the free particle streaming model of [1] to general dimensions and to an arbitrary entanglement pattern of the initial state. In more than two spacetime dimensions the spread of entanglement in these models is highly sensitive to the initial entanglement pattern, but we are able to prove an upper bound on the normalized rate of growth of entanglement entropy, and hence the tsunami velocity. The bound is smaller than what one gets for quenches in holographic theories, which highlights the importance of interactions in the spread of entanglement in many-body systems. We propose an interacting model which we believe provides an upper bound on the spread of entanglement for interacting relativistic theories. In two spacetime dimensions with multiple intervals, this model and its variations are able to reproduce intricate results exhibited by holographic theories for a significant part of the parameter space. For higher dimensions, the model bounds the tsunami velocity at the speed of light. Finally, we construct a geometric model for entanglement propagation based on a tensor network construction for global quenches.