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About this paper
Naoto Shiraishi
The authors prove that for each fixed local Hilbert-space dimension, a finite lattice size suffices to decide whether a two-dimensional, translation-invariant, nearest-neighbor Hamiltonian is frustration-free at all sizes. The cutoff exists but is not computable uniformly across dimensions. Assuming ZFC’s consistency, they also construct a commuting, diagonal Hamiltonian whose frustration-freeness ZFC cannot prove. This unprovability applies to that example.
Summary by alphaXiv.
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