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Li, W; von Delft, J; Xiang, T; Li, W (reprint author), Univ Munich, Arnold Sommerfeld Ctr Theoret Phys, Dept Phys, D-80333 Munich, Germany.
Efficient simulation of infinite tree tensor network states on the Bethe lattice
Source PublicationPHYSICAL REVIEW B
Language英语
KeywordMatrix Renormalization-group Cayley Trees Xxz Model Antiferromagnet
AbstractWe 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.
2012
ISSN1098-0121
Volume86Issue:19Pages:195137
Subject AreaPhysics
Indexed BySCI
Funding OrganizationNational Natural Science Foundation of China [10934008, 10874215]; MOST [2011CB309703]; DFG [SFB-TR12] ; National Natural Science Foundation of China [10934008, 10874215]; MOST [2011CB309703]; DFG [SFB-TR12] ; National Natural Science Foundation of China [10934008, 10874215]; MOST [2011CB309703]; DFG [SFB-TR12] ; National Natural Science Foundation of China [10934008, 10874215]; MOST [2011CB309703]; DFG [SFB-TR12]
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Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/14981
Collection理论物理所科研产出_SCI论文
Corresponding AuthorLi, W (reprint author), Univ Munich, Arnold Sommerfeld Ctr Theoret Phys, Dept Phys, D-80333 Munich, Germany.
Recommended Citation
GB/T 7714
Li, W,von Delft, J,Xiang, T,et al. Efficient simulation of infinite tree tensor network states on the Bethe lattice[J]. PHYSICAL REVIEW B,2012,86(19):195137.
APA Li, W,von Delft, J,Xiang, T,&Li, W .(2012).Efficient simulation of infinite tree tensor network states on the Bethe lattice.PHYSICAL REVIEW B,86(19),195137.
MLA Li, W,et al."Efficient simulation of infinite tree tensor network states on the Bethe lattice".PHYSICAL REVIEW B 86.19(2012):195137.
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