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Springer eBooks

Influence of Omitting the P2 Term in the Multipole Photon-Matter Hamiltonian on the Stability and Propagation

M. Yamanoi, Masamoto Takatsuji

Published Jan 1, 1978• 3 citations
Publisher
DOI
10.1007/978-1-4757-0665-9_86

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The static selector for graph-local Hamiltonians vanishes exactly at decomposition classes in which the Hamiltonian is a sum of one-site terms and graph-supported two-site terms. We give a sufficient operator-algebraic criterion for uniqueness of such an admissible-support realization, and hence for exact identification of the underlying Hilbert-space decomposition on the physical quotient. For an exact graph-local realization and an omitted site, we study the unital *-algebra generated by all one-site and graph-supported two-site terms that avoid that site. A seed-and-propagation theorem shows that if full one-site matrix control is available at a seed vertex in each connected component of the omitted-site complement and operator-Schmidt coefficients propagate that control along complement edges, then this complement algebra is the full matrix algebra on the omitted-site complement, so the omitted one-site algebra is recovered exactly as a commutant. A pairwise rigidity theorem then shows that two complement-generated exact realizations with the same recovered site-family differ only by local basis changes and subsystem permutation. Consequently, any exactly graph-local Hamiltonian with frame-stable site reconstruction has a unique admissible-support realization and exact zero-set identifiability. The hypotheses are sufficient and are stated entirely in terms of the exact graph-local realization.