Proof of Critch–Morton Conjecture 8 (SIGMA 10 (2014), 095, Section 2, p. 6): reconstruction from any consecutive three-site improper marginal
Year: 2026
Type: preprint
Abstract: We prove Critch–Morton Conjecture 8 (SIGMA 10 (2014), 095, Section 2, p. 6): every consecutive three-site improper marginalization is birational for open-boundary, translation-invariant, binary bond-two matrix product states of length N at least four. An explicit rational inverse over the complex numbers is given on a nonempty principal open domain, with both inverse identities on the affine Zariski closures. A four-by-four linear system reconstructs a three-site representation, and inverse boundary contractions restore omitted sites. Consequences include rationality in dimension seven, reconstruction from every longer consecutive block with arbitrary fixed nonzero site-dependent coherent contractions, minimality of three retained amplitude indices, and exact equations characterizing the reconstruction chart.
Authors: Ma, Haobo, Zhang, Wenlin
Institution: National University of Singapore
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225591541