arXiv 1708.093762017-08hep-th

全息纠缠密度

On Holographic Entanglement Density

Nikola I. Gushterov, Andy O'Bannon, Ronnie Rodgers

备注：: References clarified and updated compared to JHEP version
DOI：: 10.1007/JHEP10(2017)137

摘要：

我们利用全息对偶性研究了在不同时空维度$d$中的共形场论的纠缠熵，在不同的变形条件下：具有恒定源的相关洛伦兹标量算符、温度$T$、化学势$μ$、源在空间坐标中为线性的边缘洛伦兹标量算符以及圆紧化的空间方向.我们认为EE之间的条带或球体子区域和系统的其余部分，并定义的“纠缠密度”（ED）作为EE的变化，由于变形，除以子区域的体积。使用上述变形的CFTs，我们展示了ED对条带宽度或球体半径$L$的依赖性如何用于表征物质状态。例如，ED的小- $L$行为由扰动算子的维数或EE的第一定律决定。对于CFTs之间的洛伦兹不变重整化群（RG）流，“面积定理”指出EE的面积定律项的系数在UV中必须大于在IR中。在这些情况下，ED必须从下面接近零，作为$L \to \infty$。然而，当洛伦兹对称性破缺，红外不动点与紫外不动点具有不同的标度时，我们发现ED往往从上面接近热熵密度，这表明面积定理违反。

英文摘要：

We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions $d$, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature $T$, a chemical potential $μ$, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the "entanglement density" (ED) as the change in EE due to the deformation, divided by the sub-region's volume. Using the deformed CFTs above, we show how the ED's dependence on the strip width or sphere radius, $L$, is useful for characterizing states of matter. For example, the ED's small-$L$ behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the "area theorem" states that the coefficient of the EE's area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as $L \to \infty$. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文