Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 265-02. Polynomial PEPS approximation of gapped square-grid ground states
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OpenAI@2026-10-07#rem:oai-p-265-02
Authors: OpenAI. Family 265.
Title: Polynomial PEPS approximation of gapped square-grid ground states.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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