Simulation of three-dimensional quantum systems with projected entangled-pair states

The iPEPS ansatz section describes six D-dimensional auxiliary indices for a 3D tensor, and the Introduction says the additional legs increase computational cost. Section III reports that a large-cluster contraction typically is feasible only at D = 2. But the paper does not characterize 3D iPEPS as generally impractical: its Summary presents a practical method at reasonable cost. It also uses d for the local physical-index dimension, not spatial dimension. (LLM, conf=0.87)

Section III (p. 205137-3) says small 3D cluster contractions neglect loops and that larger clusters have steep costs, reaching O(D^29). The Summary and Discussion (p. 205137-9) says a cluster update would cost more than simple update, but does not establish that incorporating local loops causes severe scaling for neighborhood updates specifically; the quantified scaling is for contractions. (LLM, conf=0.86)

Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

Section IV describes a double-layer boundary-iPEPS contraction, and the Heisenberg-model section reports simulations through D = 4. The paper also reports steep computational scaling, but it does not state that the scheme is impractical beyond D = 4; D = 4 is the largest value tested there. (LLM, conf=0.82)