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arXiv AI By Mahmud Ashraf Shamim, Md Moshiur Rahman Raj, Mohamed Hibat-Allah, Ruy Fabila-Monroy, Nobuchika Okada, Paulo T. Araujo

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

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The paper presents a graph-theoretic framework for analyzing Heisenberg antiferromagnets, where the Hamiltonian in a fixed-magnetization sector is represented as a constant minus the weighted Laplacian of a Hilbert graph (HG). The ground-state energy is linked to the largest eigenvalue of this Laplacian, equivalent to a spectral relaxation of weighted Max‑Cut on the HG, while the phase-dependent part of the variational energy maps to an antiferromagnetic XY model on the same graph. Restricting to real variational states reduces the problem to an Ising model, and the optimal sign structure of the ground state can be recovered in polynomial time from the HG weights, with the bipartiteness of the HG determining whether a diagonal sign transformation can eliminate all positive off-diagonal elements.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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