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Generalized Lanczos method for systematic optimization of tensor network states |
| Rui-Zhen Huang(黄瑞珍)1,2, Hai-Jun Liao(廖海军)1, Zhi-Yuan Liu(刘志远)2,3, Hai-Dong Xie(谢海东)1,2, Zhi-Yuan Xie(谢志远)4, Hui-Hai Zhao(赵汇海)5,6,7, Jing Chen(陈靖)1,2, Tao Xiang(向涛)1,2,8 |
1 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
4 Department of Physics, Renmin University of China, Beijing 100872, China;
5 Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;
6 Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan;
7 RIKEN Brain Science Institute, Wako-shi, Saitama 351-0198, Japan;
8 Collaborative Innovation Center of Quantum Matter, Beijing 100190, China |
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Abstract We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.
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Received: 08 March 2018
Revised: 20 April 2018
Accepted manuscript online:
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PACS:
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05.10.Cc
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(Renormalization group methods)
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05.10.-a
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(Computational methods in statistical physics and nonlinear dynamics)
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05.30.-d
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(Quantum statistical mechanics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11190024 and 11474331). |
Corresponding Authors:
Tao Xiang
E-mail: txiang@iphy.ac.cn
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Cite this article:
Rui-Zhen Huang(黄瑞珍), Hai-Jun Liao(廖海军), Zhi-Yuan Liu(刘志远), Hai-Dong Xie(谢海东), Zhi-Yuan Xie(谢志远), Hui-Hai Zhao(赵汇海), Jing Chen(陈靖), Tao Xiang(向涛) Generalized Lanczos method for systematic optimization of tensor network states 2018 Chin. Phys. B 27 070501
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