Efficient simulation of infinite tree tensor network states on the Bethe lattice

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	Efficient simulation of infinite tree tensor network states on the Bethe lattice
	Xiang, T
刊名	PHYSICAL REVIEW B
	2012
卷号	86 期号:19 页码:195137
关键词	MATRIX RENORMALIZATION-GROUP CAYLEY TREES XXZ MODEL ANTIFERROMAGNET
ISSN号	1098-0121
通讯作者	Li, W (reprint author), Univ Munich, Arnold Sommerfeld Ctr Theoret Phys, Dept Phys, D-80333 Munich, Germany.
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.
学科主题	Physics
收录类别	SCI
资助信息	National Natural Science Foundation of China [10934008, 10874215]; MOST [2011CB309703]; DFG [SFB-TR12]
原文出处	http://dx.doi.org/10.1103/PhysRevB.86.195137
语种	英语
WOS记录号	WOS:000311544500005
公开日期	2014-04-25
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/14981]
专题	理论物理研究所_理论物理所1978-2010年知识产出
推荐引用方式 GB/T 7714	Xiang, T. Efficient simulation of infinite tree tensor network states on the Bethe lattice[J]. PHYSICAL REVIEW B,2012,86(19):195137.
APA	Xiang, T.(2012).Efficient simulation of infinite tree tensor network states on the Bethe lattice.PHYSICAL REVIEW B,86(19),195137.
MLA	Xiang, T."Efficient simulation of infinite tree tensor network states on the Bethe lattice".PHYSICAL REVIEW B 86.19(2012):195137.