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
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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