フズケされたヒへイスナー・アンフェリーノメチックスのウェイブフォंक्शन (HAF) の相構造についてのグラフォティクアナlyシスティック：ヴァリエーション・ウェイブファンクショングラフツ(GHG)に基づく Max-Cut インスタンスとしての相の復元

arXiv:2602.04943v2 Announce Type: replace-cross Abstract: Despite extensive study, the phase structure of the wavefunctions in frustrated Heisenberg antiferromagnets (HAF) is not yet systematically characterized. In this work, we represent the Hilbert space of an HAF as a weighted graph, which we term the Hilbert graph (HG), whose vertices are spin configurations and whose edges are generated by off-diagonal spin-flip terms of the Heisenberg Hamiltonian, with weights set by products of wavefunction amplitudes. Holding the amplitudes fixed and restricting phases to $\mathbb{Z}_2$ values, the phase-dependent variational energy can be recast as a classical Ising antiferromagnet on the HG, so that phase reconstruction of the ground state reduces to a weighted Max-Cut instance. This shows that phase reconstruction HAF is worst-case NP-hard and provides a direct link between wavefunction sign structure and combinatorial optimization.