O（N）模型中的纠缠熵
Entanglement Entropy in the O(N) model
摘要：
一般认为，在空间维度d > 1时，对纠缠熵S = - tr rho_A log rho_A的主要贡献与子系统A的边界面积成比例。这个“面积定律”的系数是非普适的。然而，在量子临界点附近，S被认为具有次主导的普适修正。本文研究了1 < d < 3时量子O（N）模型中的纠缠熵。我们使用一个扩展在n = 3-d来评估i）的通用几何校正S沿圆形边界划分的无限圆柱; ii）由于一个有限的相关长度的通用校正S。两种修正在Wilson-Fisher和Gaussian不动点上是不同的，Wilson-Fisher不动点的λ-> 0极限不同于Gaussian不动点。此外，我们还计算了Renyi熵S_n =（log tr rho^n_A）/（1-n）在n阶和大N阶展开式下的相关长度修正。对于N ->无穷大，这种修正通常按N^2而不是天真地期望的N来缩放。此外，对于d接近3，Renyi熵具有作为n的函数的相变。
英文摘要：
It is generally believed that in spatial dimension d > 1 the leading contribution to the entanglement entropy S = - tr rho_A log rho_A scales as the area of the boundary of subsystem A. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a quantum critical point S is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum O(N) model in 1 < d < 3. We use an expansion in epsilon = 3-d to evaluate i) the universal geometric correction to S for an infinite cylinder divided along a circular boundary; ii) the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the epsilon -> 0 limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy S_n = (log tr rho^n_A)/(1-n) in epsilon and large-N expansions. For N -> infinity, this correction generally scales as N^2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.
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