Accurate determination of tensor network state of quantum lattice models in two dimensions

Abstract

We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach which applies iteratively the Trotter-Suzuki decomposition of the projection operator and the singular value decomposition of matrix. The norm of the wavefunction and the expectation value of a physical observable are evaluated by a coarse grain renormalization group approach. Our method allows a tensor-network wavefunction with a high bond degree of freedom (such as D=8) to be handled accurately and efficiently in the thermodynamic limit. For the Heisenberg model on a honeycomb lattice, our results for the ground state energy and the staggered magnetization agree well with those obtained by the quantum Monte Carlo and other approaches.

4 pages 5 figures 2 tables

References in corpus (3)

• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Tensor renormalization group approach to 2D classical lattice models

Cited by in corpus (3)

• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States