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A translation-invariant MERA, characterized by one disentangler and one isometry at each layer, need not represent a translation-invariant state |Ψ, hence the need to consider the average density matrix ρ̄.
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A translation-invariant MERA, characterized by one disentangler and one isometry at each layer, need not represent a translation-invariant state |Ψ, hence the need to consider the average density matrix ρ̄.
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Each operator ρτ in Eq. 16 is both Hermitian (ρτ† = ρτ) and non-negative (| ρτ |0,) but its trace is tr (ρτ) = χT. For simplicity, we call ρτ a density matrix for any χT 1, even though it is only a proper density matrix for χT =1.
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Each operator ρτ in Eq. 16 is both Hermitian (ρτ† = ρτ) and non-negative (| ρτ |0,) but its trace is tr (ρτ) = χT. For simplicity, we call ρτ a density matrix for any χT 1, even though it is only a proper density matrix for χT =1.
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We note that the χ=22 simulation for the Ising model gives less accurate results than the trend line observed for smaller χ in Fig. 24 would suggest. It is possible that numerical errors (such as errors in the sparse eigenvalue decomposition used) may have been significant at this level of accuracy.
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We note that the χ=22 simulation for the Ising model gives less accurate results than the trend line observed for smaller χ in Fig. 24 would suggest. It is possible that numerical errors (such as errors in the sparse eigenvalue decomposition used) may have been significant at this level of accuracy.
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