论文标题
与固定区域状态的全息纠缠熵的探测相变
Probing phase transitions of holographic entanglement entropy with fixed area states
论文作者
论文摘要
最近的结果表明，应在相关的ryu-takayanagi（RT）表面近相变的全息纠缠熵的新校正。我们通过将批量状态分解为固定区域，并猜测将保持某些“对角线近似”来研究此类校正。就牛顿常数$ g $而言，这可以在此类过渡附近的订单$ o（g^{ - 1/2}）$进行更正，特别是大于批量量子字段的通用更正。但是，校正被指数抑制了过渡。净效应是使纠缠成为所有参数的平滑函数，将RT“相变”转变为已经在此分析级别的交叉。 我们通过在ADS $ _3 $真空边界上的一对断开间隔和在BTZ黑洞边界上的一个间隔上给出的边界区域的显式计算（再次假设我们的对角线近似）来说明这种效果。在我们的对角线近似清楚地达到的自然大批量极限中，第二个示例验证了我们的结果与Murthy和Srednicki在混乱的多体系统的背景下做出的一般预测一致。作为对我们猜想的对角线近似的进一步检查，我们表明它还重现了$ o（g^{ - 1/2}）$校正，发现Penington等人用于类似的量子RT转变。我们的显式计算还说明了RT-ARAES波动的截止依赖性。
Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain `diagonal approximation' will hold. In terms of the bulk Newton constant $G$, this yields a correction of order $O(G^{-1/2})$ near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT `phase transition' into a crossover already at this level of analysis. We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS$_3$ vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the $O(G^{-1/2})$ correction found Penington et al for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.
