Science Advances

Supplementary Materials

This PDF file includes:

  • Section S1. Tensor contractions in the Grassmann formalism
  • Section S2. Matchgates and fermionic Gaussian states
  • Section S3. Conversion of generating matrices to covariance matrices
  • Section S4. Contraction rules for generating matrices
  • Section S5. Explicit generating matrices and numerical results
  • Fig. S1. Combining tiles of matchgates.
  • Fig. S2. Tile orientations under contraction.
  • Fig. S3. Constructing the mMERA.
  • Fig. S4. Energy convergence of the mMERA.
  • Fig. S5. Determining scaling dimensions of flat tilings.
  • Fig. S6. Determining scaling dimensions of hyperbolic tilings.
  • Fig. S7. Determining scaling dimensions of mMERA.
  • Fig. S8. Determining structure constants.
  • Fig. S9. Correlations and entanglement with IR cutoff.
  • Fig. S10. Construction of triangle states with bond dimension χ = 2, 4, 8.
  • Table S1. Values of the critical generating matrix parameter a for different {3, k} triangular tilings and ultraviolet cutoffs.
  • Table S2. Exact conformal scaling dimension of various (quasi-)primary fields ϕ of the Ising CFT.
  • References (4451)

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