论文标题
单独装饰的钻石晶格和两个4级平面晶格的AKLT型号被覆盖
The AKLT models on the singly decorated diamond lattice and two degree-4 planar lattices are gapped
论文作者
论文摘要
最近，已经显示出各种2D AKLT模型被散布在六角形晶格上。在这里，我们报告了一个非平凡的3D AKLT模型，该模型由钻石晶格位点上的Spin-2实体组成，每个相邻的Spin-2位点之间的一个单个SPIN-1实体。尽管对于钻石和方形晶格上均匀的Spin-2 AKLT模型的非零差距问题仍然开放，但我们能够确定两个平面晶格的间隙的存在，我们分别称其为刻有的正方形晶格和三角形 - octagon-octagon lattice。到目前为止，后两个模型是仅有的两个均匀的自旋2 AKLT模型，它们具有可证明的非零差距以上底态。我们还讨论了一些尝试证明广场和Kagome晶格上存在差距的尝试。此外，我们表明，如果一个人可以解决加权AKLT Hamiltonian的有限大小问题，并且差距大于某些阈值，则方格上的模型将夹在热力学极限中。差距的阈值与有限大小的问题的线性大小成反比。
Recently various 2D AKLT models have been shown to be gapped, including the one on the hexagonal lattice. Here we report on a non-trivial 3D AKLT model which consists of spin-2 entities on the diamond lattice sites and one single spin-1 entity between every neighboring spin-2 site. Although the nonzero gap problem for the uniformly spin-2 AKLT models on the diamond and square lattices is still open, we are able to establish the existence of the gap for two planar lattices, which we call the inscribed square lattice and the triangle-octagon lattice, respectively. So far, these latter two models are the only two uniformly spin-2 AKLT models that have a provable nonzero gap above the ground state. We also discuss some attempts in proving the gap existence on both the square and kagome lattices. In addition, we show that if one can solve a finite-size problem of a weighted AKLT Hamiltonian and if the gap is larger than certain threshold, then the model on the square lattice is gapped in the thermodynamic limit. The threshold of the gap scales inversely with the linear size of the finite-size problem.
