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2 results

  • 14 - Classical Transfer Matrix Renormalization

  • 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 217-233

  • Summary

    This chapter introduces two kinds of RG methods for solving the leading eigenvalue and eigenvectors of a transfer matrix: TMRG (transfer matrix renormalization group) and CTMRG (corner transfer matrix renormalization group). These methods are developed to study the thermodynamic properties of two-dimensional classical statistical models. Furthermore, in the framework of MPS, the fixed-point equations of these methods are derived, and the steps for efficiently solving these equations are outlined.

  • 17 - MPS Solution of QTMRG

  • 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 258-272

  • Summary

    This chapter reformulates QTMRG using the language of MPS and introduces the concept of bicanonical MPS and the method of biorthogonalization. The fixed-point equations for determining the local tensors of MPS in a translation-invariant system of one or more than one site in a unit cell are derived. The steps for solving these equations in the scheme of biorthonormalization are discussed.