Variational Monte Carlo simulations using tensor-product projected states
arXiv:1407.4107 · doi:10.1103/PhysRevB.91.165113
Abstract
We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.
7 pages, 5 figures, published version
References in corpus (10)
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Valence Bond Solids for Quantum Computation
- Tensor-entanglement renormalization group approach to 2D quantum systems
- Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
- Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
- Strings, Projected Entangled Pair States, and variational Monte Carlo methods
- Monte Carlo simulation with Tensor Network States
- Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
- Assessing the accuracy of projected entangled-pair states on infinite lattices
- Renormalization algorithm with graph enhancement