Bethe格上无限树张量网络状态的高效模拟
Efficient simulation of infinite tree tensor network states on the Bethe lattice
摘要：
我们表明，江等提出的简单的更新方法。[H.C.姜志毅Weng和T. Xiang，Phys. Rev. Lett. 101，090603（2008）]是一种用于确定Bethe晶格上的无限树张量网络状态的有效且准确的方法。研究了Bethe格点上量子横向伊辛模型和海森堡XXZ模型的基态性质.发现横向伊辛模型经历二阶量子相变，磁化率发散，但关联长度有限，即使在相变点（q为Bethe晶格的坐标数）也有1/ln（q-1）的上限.对这一奇特的“临界”现象给出了直观的解释。Bethe晶格上的XXZ模型在各向同性点发生一级量子相变。此外，简单的更新方案被发现与Bethe近似。最后，通过将简单的更新应用于各种树张量聚类，我们可以获得二维格的相当好的和可扩展的近似。
英文摘要：
We show that the simple update approach proposed by Jiang et. al. [H.C. Jiang, Z.Y. Weng, and T. Xiang, Phys. Rev. Lett. 101, 090603 (2008)] is an efficient and accurate method for determining the infinite tree tensor network states on the Bethe lattice. Ground state properties of the quantum transverse Ising model and the Heisenberg XXZ model on the Bethe lattice are studied. The transverse Ising model is found to undergo a second-order quantum phase transition with a diverging magnetic susceptibility but a finite correlation length which is upper-bounded by 1/ln(q-1) even at the transition point (q is the coordinate number of the Bethe lattice). An intuitive explanation on this peculiar "critical" phenomenon is given. The XXZ model on the Bethe lattice undergoes a first-order quantum phase transition at the isotropic point. Furthermore, the simple update scheme is found to be related with the Bethe approximation. Finally, by applying the simple update to various tree tensor clusters, we can obtain rather nice and scalable approximations for two-dimensional lattices.
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