Department of Physics, University of California, Berkeley, California 94720, USA.
Phys Rev Lett. 2011 Jul 8;107(2):020402. doi: 10.1103/PhysRevLett.107.020402. Epub 2011 Jul 5.
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.
普适对数项出现在一维（1D）的量子临界点（QCP）中，并且已经在二维（2D）中由二维共形场理论描述的 QCP 中被预测到。在这种 QCP 下，通过具有开放边界条件的一维自旋链的“香农熵”可以获得条带几何中的纠缠熵。发现 XXZ 链的香农熵具有对数项，这意味着对于正方形晶格量子二聚体模型的 QCP，具有普适系数±0.25 的对数。然而，横向场伊辛模型的香农熵中的对数，对应于二维伊辛共形 QCP 中的纠缠，发现其对 replica 或 Renyi 指数的依赖具有奇异的依赖性，这是由于在纠缠切割处流向不同边界条件的流动所导致的。
