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2 results

  • 8 - Implementation of Symmetries

  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book:
    Density Matrix and Tensor Network Renormalization
    Published online:
    18 January 2024
    Print publication:
    31 August 2023, pp 123-136

  • Summary

    Implementation of symmetries can significantly enhance the expression power of DMRG and effectively allow us to retain more basis states in the DMRG calculation. This chapter discusses the skills of imposing symmetries, including spin reflection, spatial reflection, continuous U(1) or other symmetries with additive quantum numbers, and non-Abelian SU(2) symmetry, in a DMRG calculation.

  • 10 - Matrix Product States

  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book:
    Density Matrix and Tensor Network Renormalization
    Published online:
    18 January 2024
    Print publication:
    31 August 2023, pp 154-165

  • Summary

    This chapter discusses the properties of matrix product state (MPS). It starts with a simple proof that the wave function generated by DMRG is an MPS. Then three different but equivalent canonical forms or representations of MPS are introduced. An MPS generally has redundant gauge degrees of freedom on each bond linking two neighboring local tensors. One can convert it into a canonical form by taking a canonical transformation to remove the gauge redundancy in the local tensors. Finally, the implementation of symmetries, including both the U(1) and SU(2) symmetries, is discussed.