Graph-Theoretic Formulation of Hamiltonian and Ground-State Sign Structures in Heisenberg Antiferromagnets

arXiv:2602.04943v5 Announce Type: replace-cross Abstract: We study Heisenberg antiferromagnets through a graph-theoretic representation of their Hamiltonians. In the computational basis of a fixed-magnetization sector, the Heisenberg Hamiltonian equals a constant minus the weighted Laplacian of a graph whose vertices are spin configurations and whose edges connect configurations related by exchanging two antiparallel spins on a lattice bond. We call this graph the Hilbert graph (HG) which is isomorphic to the token graph of the lattice over which the Hamiltonian is defined. The exact ground-st

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