Tensor Network States and Geometry

@article{Evenbly2011TensorNS,
  title={Tensor Network States and Geometry},
  author={G. Evenbly and G. Vidal},
  journal={Journal of Statistical Physics},
  year={2011},
  volume={145},
  pages={891-918}
}
  • G. Evenbly, G. Vidal
  • Published 2011
  • Mathematics, Physics
  • Journal of Statistical Physics
  • Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional… CONTINUE READING
    192 Citations
    Holographic geometries of one-dimensional gapped quantum systems from tensor network states
    • 11
    • Highly Influenced
    • PDF
    Entanglement, tensor networks and black hole horizons
    • 19
    • Highly Influenced
    • PDF
    Tensor networks for complex quantum systems
    • 68
    • PDF

    References

    SHOWING 1-10 OF 91 REFERENCES
    Accurate determination of tensor network state of quantum lattice models in two dimensions.
    • 166
    • PDF