论文标题
全息纠缠熵探针在自发对称性上与矢量顺序断裂
Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order
论文作者
论文摘要
我们研究了从爱因斯坦-SU（2）Yang-Mills理论获得的5维带电的黑色勃雷几何形状中的全息纠缠熵。该重力系统在其临界点附近经历了二阶相变，该临界点受阳米尔斯字段的空间成分影响，这是溶液的正常模式。这被称为各向同性和各向异性相之间的相变。我们通过利用Arxiv：1109.4592中给出的散装时空几何形状的溶液来获得全息纠缠熵的分析解，我们考虑了在ADS边界上定义的子系统，其形状宽，薄板和圆柱体。事实证明，临界点附近的纠缠熵显示了缩放行为，因此对于平板和圆柱体，$δ__\ varepsilon s \ sim \ sim \ left（1- \ frac {t} {t_c} {t_c} \ right） s^{iso} -s^{aniso} $，$ s^{iso} $表示在各向同性阶段中的纠缠熵，而$ s^{aniso} $表示在各向异性阶段中表示。我们建议一个数量$ o_ {12} \ equiv s_1-s_2 $作为临界点附近的新订单参数，当平板垂直于向量订单的方向时，$ s_1 $是纠缠的熵，而$ s_2 $是当平板平行于向量订单时。 $ o_ {12} = 0 $在各向同性阶段，但在各向异性阶段，顺序参数变为非零，显示相同的缩放行为。最后，我们表明，即使在关键点附近，纠缠熵的第一定律也是持有的。尤其是，我们发现气缸的纠缠温度为$ \ Mathcal t_ {cy} = \ frac {c_ {ent}}} {a} $，其中$ c_ {ent} = 0.163004 \ pm0.000001 $和$ a $是气缸的半径。
We study holographic entanglement entropy in 5-dimensional charged black brane geometry obtained from Einstein-SU(2)Yang-Mills theory defined in asymptotically AdS space. This gravity system undergoes second order phase transition near its critical point affected by a spatial component of the Yang-Mills fields, which is normalizable mode of the solution. This is known as phase transition between isotropic and anisotropic phases. We get analytic solutions of holographic entanglement entropies by utilizing the solution of bulk spacetime geometry given in arXiv:1109.4592, where we consider subsystems defined on AdS boundary of which shapes are wide and thin slabs and a cylinder. It turns out that the entanglement entropies near the critical point shows scaling behavior such that for both of the slabs and cylinder, $Δ_\varepsilon S\sim\left(1-\frac{T}{T_c}\right)^β$ and the critical exponent $β=1$, where $Δ_\varepsilon S\equiv S^{iso}-S^{aniso}$, and $S^{iso}$ denotes the entanglement entropy in isotropic phase whereas $S^{aniso}$ denotes that in anisotropic phase. We suggest a quantity $O_{12}\equiv S_1-S_2$ as a new order parameter near the critical point, where $S_1$ is entanglement entropy when the slab is perpendicular to the direction of the vector order whereas $S_2$ is that when the slab is parallel to the vector order. $O_{12}=0$ in isotropic phase but in anisotropic phase, the order parameter becomes non-zero showing the same scaling behavior. Finally, we show that even near the critical point, the first law of entanglement entropy is hold. Especially, we find that the entanglement temperature for the cylinder is $\mathcal T_{cy}=\frac{c_{ent}}{a}$, where $c_{ent}=0.163004\pm0.000001$ and $a$ is the radius of the cylinder.
