Tensor Network States and Geometry

  title={Tensor Network States and Geometry},
  author={Glen Evenbly and Guifr{\'e} Vidal},
  journal={Journal of Statistical Physics},
  • G. Evenbly, G. Vidal
  • Published 6 June 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… 
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