Establishing Néel order in the square-lattice antiferromagnetic Heisenberg model: a bootstrap proof
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arXiv: 2611.03241v1 · Summary page
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A familiar magnetic pattern gets a rigorous foundation
The square-lattice antiferromagnetic Heisenberg model is a standard description of quantum magnetism, yet its expected Néel order—an alternating arrangement of magnetic moments—has resisted rigorous proof in the case studied here. A new theoretical preprint reports such a proof using a bootstrap approach: mathematical consistency constraints bound the correlations that the system can possess.
The authors combine inequalities connecting long-range order to short-distance correlations with certified energy bounds derived from matrix product states. This yields a strictly positive lower bound on the order parameter at the isotropic Heisenberg point and at selected anisotropies in a related model. Beyond settling a foundational question, the work shows how computational tools can help produce mathematical certificates rather than numerical evidence alone.
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