Entanglement negativity and sudden death in the toric code at finite temperature
Entanglement negativity and sudden death in the toric code at finite temperature
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DOI：
10.1103/physrevb.97.144410
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发表时间：
2018-04-16
影响因子：
3.7
通讯作者：
Castelnovo, C.
中科院分区：
文献类型：
--
作者：
Hart, O.;Castelnovo, C.
利用对数纠缠负性研究了二维环面码中量子关联在有限温度下的命运。我们能够获得精确的结果，让我们深入了解热激发如何影响量子纠缠。复曲面代码有两种类型的基本激励（缺陷）消耗不同的能量。我们发现，一个O（1）密度的较低的能量缺陷是需要降低零温度纠缠的两个子系统之间的相互接触。然而，仅一种类型的激发不足以杀死所有的量子相关性，并且需要O（1）密度的较高能量缺陷来引起所谓的负性突然死亡。有趣的是，如果其中一个激发的能量消耗达到无穷大，量子相关性在任意高温下都存在，这一特征可能与其他量子自旋液体和一般受挫折的系统共享，当投射到它们的低能态时。我们证明了这种行为的小的子系统，我们可以证明，负性是一个必要和充分条件的可分性，以及扩展的子系统，它只是一个必要条件。我们进一步观察到，在给定的温度下，每个边界自由度的负性随着边界的大小而增加（参数化），并且具有扩展边界的子系统之间的量子关联对热波动更鲁棒。
We study the fate of quantum correlations at finite temperature in the two-dimensional toric code using the logarithmic entanglement negativity. We are able to obtain exact results that give us insight into how thermal excitations affect quantum entanglement. The toric code has two types of elementary excitations (defects) costing different energies. We show that an O (1) density of the lower energy defect is required to degrade the zero-temperature entanglement between two subsystems in contact with one another. However, one type of excitation alone is not sufficient to kill all quantum correlations, and an O (1) density of the higher energy defect is required to cause the so-called sudden death of the negativity. Interestingly, if the energy cost of one of the excitations is taken to infinity, quantum correlations survive up to arbitrarily high temperatures, a feature that is likely shared with other quantum spin liquids and frustrated systems in general, when projected down to their low-energy states. We demonstrate this behavior both for small subsystems, where we can prove that the negativity is a necessary and sufficient condition for separability, as well as for extended subsystems, where it is only a necessary condition. We further observe that the negativity per boundary degree of freedom at a given temperature increases (parametrically) with the size of the boundary, and that quantum correlations between subsystems with extended boundaries are more robust to thermal fluctuations.