A generalized Lanczos method for systematic optimization of tensor network states

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 both the accuracy and the efficiency of the tensor-network algorithm and allows the ground state to be determined accurately using TNS with very small virtual bond dimensions. This state 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.

arXiv comment5 pages, 5 figures

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Cited by in corpus (10)

• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Accurate simulation for finite projected entangled pair states in two dimensions
• Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks
• Theory of competing Chern-Simons orders and emergent phase transitions
• Shortcut Matrix Product States and its applications
• Combination of Tensor Network States and Green's function Monte Carlo
• Generalized Lanczos method for systematic optimization of neural-network quantum states
• Bundled matrix product states represent low-energy excitations faithfully
• A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces