Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2010 Jul 30;105(5):050502. doi: 10.1103/PhysRevLett.105.050502.
Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size L in d spatial dimensions is S∼L(d-1)logL, a result that should be contrasted with the usual boundary law S∼L(d-1). This term depends only on the geometry of the Fermi surface and on the boundary of the region in question. I give an intuitive account of this anomalous scaling based on a low energy description of the Fermi surface as a collection of one-dimensional gapless modes. Using this picture, I predict a violation of the boundary law in a number of other strongly correlated systems.
具有有限费米面的自由费米子已知会表现出异常大的纠缠熵。在 d 维空间中，线性尺寸为 L 的区域的纠缠熵的主要贡献为 S∼L(d-1)logL，这一结果与通常的边界定律 S∼L(d-1)形成对比。这个项仅取决于费米面的几何形状和所讨论区域的边界。我基于费米面的低能描述，即一维无间隙模式的集合，给出了对这种异常标度的直观解释。利用这一图像，我预测在一些其他强关联系统中会违反边界定律。
