2012/09/30 by Wei Li, Jan von Delft, Tao Xiang · 1 citation
Mathematics · Physics and Astronomy · #Bethe lattice #Ising model #Lattice (music) #Mathematical physics #Mathematics #Phase transition #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.86.195137
published as Phys. Rev. B 86, 195137 (2012) · 9 pages, 10 figures
openalex publication_date 2012/11/26 · arxiv created 2012/11/27 · arxiv updated 2012/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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\ensuremath-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.