Entanglement renormalization, scale invariance, and quantum criticality

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In Ref. [ 7 ] the ascending/descending/scaling superoperators were called quantum MERA channel/MERA transfer matrix. We emphasize that these superoperators, an essential part of the MERA formalism, were introduced in Ref. [ 5 ] (see e.g. Fig. 5 of Ref. [ 5 ] for an explicit construction of the descending superoperator, where it is also evident that it is a quantum channel)

Cited in the paper.

Our numerics show that the lowest n Δ n_{\Delta} scaling dimensions fulfill Δ α ( 1 ) ≈ Δ α ≈ Δ α CFT \Delta^{(1)}_{\alpha}\approx\Delta_{\alpha}\approx\Delta_{\alpha}^{\mbox{\tiny CFT}} , where n Δ n_{\Delta} grows with χ \chi

Cited in the paper.

Alternatively, the central charge c c can be evaluated from the two- and three-point correlator of the stress energy tensor [ 9 , 10 ] as explored elsewhere (J.I. Latorre, private communication )

Cited in the paper.

In practice we only compute the first k k terms ( k ≈ 2 , 3 k\approx 2,3 ) of the expansion h ¯ = h 0 + h 1 / 3 + h 2 / 9 + ⋯ \bar{h}=h_{0}+h_{1}/3+h_{2}/9+\cdots . This average is only needed when H H contains operators that are irrelevant in the RG sense

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