Exact rainbow tensor networks for the colorful Motzkin and Fredkin spin chains
Exact rainbow tensor networks for the colorful Motzkin and Fredkin spin chains
复制标题
DOI：
10.1103/physrevb.100.214430
复制
发表时间：
2019-12-24
影响因子：
3.7
通讯作者：
Klich, Israel
中科院分区：
文献类型：
--
作者：
Alexander, Rafael N.;Ahmadain, Amr;Klich, Israel
我们提出了体张量网络，它准确地表示了一维无挫折哈密顿量的连续族的基态。这些态，即面积变形的Motzkin态和Fredkin态，表现出一种新的量子相变。通过调节单个参数，它们从服从面积定律的相变成高度纠缠的彩虹相，在彩虹相中，半链熵随着体积的增大而变化。将这些基态表示为随机游动的叠加，我们为这些基态引入张量网络，其中步行者的局部和整体规则被烘焙成整体张量，从而提供了对基态(其中一些满足纠缠熵的体积律标度)的有效描述。
We present bulk tensor networks that exactly represent the ground states of a continuous family of one-dimensional frustration-free Hamiltonians. These states, which are known as area-deformed Motzkin and Fredkin states, exhibit a novel quantum phase transition. By tuning a single parameter, they go from a phase obeying an area law to a highly entangled "rainbow" phase, where the half-chain entropy scales with the volume. Using the representation of these ground states as superpositions of random walks, we introduce tensor networks for these ground states where local and global rules of the walker are baked into bulk tensors, thereby providing an efficient description of the ground states (some of which satisfy a volume law scaling of entanglement entropy).