Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological entropy from analytical calculations or numerical simulations is generally difficult due to the fact that it is an order one correction to leading terms that scale with the size of the system. In order to distil the topological entropy, one resorts to extrapolation as a function of system size, or to clever subtraction schemes that allow to cancel out the leading terms. Both approaches have the disadvantage of requiring multiple (accurate) calculations of the entanglement of the system. Here we propose a modification of conventional entanglement calculations that allows to obtain the topological entropy of a system from a single measurement of entanglement. In our approach, we replace the conventional trace over the degrees of freedom of a partition of the system with a projection onto a given state (which needs not be known). We show that a proper choice of partition and projective measurement allows to rid the entanglement measures of the typical boundary terms, thus exposing the topological contribution alone. We consider specifically the measures known as von Neumann entropy and entanglement negativity, and we discuss their application to both models that exhibit quantum as well as classical topological order.
Corner entanglement scaling with projected entangled pair states
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；International Solvay Institutes（国际索尔维研究所）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
Optimization of infinite projected entangled pair states: The role of multiplets and their breaking
无限投射纠缠对态（iPEPS）技术[J. Jordan { \it et al.}，物理修订信函{ \bf 101}，250602（2008）]近年来已被广泛用于评估直接在热力学极限下工作的二维量子系统的性质。这种基于基态波函数的张量网络表示的形式主义具有几个吸引人的特征，例如，通过构造对所谓的纠缠熵的面积定律进行编码;然而，该方法在处理张量的优化时提出了关键问题，以便找到对给定哈密顿量的精确基态的最佳可能近似。在这里，我们讨论了在所谓的简单和完整的更新内的时间演化优化中出现的障碍，并将它们与张量的“虚拟”指数中出现的尖锐多重态结构联系起来。在这种情况下，键尺寸$D$的一般选择与多重态不相容，并导致对称性破缺（例如，产生有限磁序）。此外，改变初始猜测，可以达到不同的最终状态，磁化值具有非常大的偏差。为了验证这种行为，我们显示的结果的$S=1/2$海森堡模型的一个阵列上的耦合的梯子，其中一个消失的磁化低于临界interladder耦合恢复仅为选定的值的$D$，而一个盲目的优化与通用的$D$产生一个有限的磁化下降到极限的解耦的梯子。
