Manuscript Oai265-A@2 · Oai265-A.tex · remark · c0a34a45

Remark: A polynomial bond bound is not the same numerical area law

Stage 3: PEPS existence, algorithms, and approximation budgets › The actual consequence of a tensor cut · lines 826–836

If $D_{L} \leq C_{P} L^{c_{P}}$ , the direct cut argument gives

S_{Ψ_{L}} (A) \leq ∣ \partial_{Λ} A ∣ (lo g C_{P} + c_{P} lo g L) .

The extra $lo g L$ is not the uniform constant asserted in 265-01. No equivalence between the two external statements is proved by this cut argument.

Displayed formulas in this passage

unlabeled · line 828
$S_{Ψ_{L}} (A) \leq ∣ \partial_{Λ} A ∣ (lo g C_{P} + c_{P} lo g L) .$