{"id":"openai-math/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states","pdf":"https://github.com/openai/math/blob/main/preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026","tags":["quantum-many-body","tensor-networks","condensed-matter"],"score":0,"title":"Polynomial PEPS approximation of gapped square-grid ground states","domain":"Mathematical physics","family":"265","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove that the unique ground state of a uniformly gapped nearest-neighbor Hamiltonian on an $`L\\times L`$ square lattice admits a projected entangled-pair state approximation with bond dimension polynomial in L and global vector error at most L −1 after normalization. Only the gap of the full Hamiltonian is assumed. The result is an existence theorem, with constants uniform over Hamiltonians of fixed local dimension, interaction strength, and gap.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Area laws and tensor networks for two-dimensional gapped systems"}