[2602.04943] Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets

Condensed Matter > Strongly Correlated Electrons arXiv:2602.04943 (cond-mat) [Submitted on 4 Feb 2026 (v1), last revised 7 Apr 2026 (this version, v3)] Title:Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets Authors:Mahmud Ashraf Shamim, Md Moshiur Rahman Raj, Mohamed Hibat-Allah, Paulo T Araujo View a PDF of the paper titled Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets, by Mahmud Ashraf Shamim and 3 other authors View PDF HTML (experimental) Abstract:We study the computational complexity of learning the ground state phase structure of Heisenberg antiferromagnets. Representing Hilbert space as a weighted graph, the variational energy defines a weighted XY model that, for $\mathbb{Z}_2$ phases, reduces to a classical antiferromagnetic Ising model on that graph. For fixed amplitudes, reconstructing the signs of the ground state wavefunction thus reduces to a weighted Max-Cut instance. This establishes that ground state phase reconstruction for Heisenberg antiferromagnets is worst-case NP-hard and links the task to combinatorial optimization. Comments: Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Quantum Physics (quant-ph) Cite as: arXiv:2602.04943 [cond-mat.str-el]   (or arXiv:2602.04943v3 [cond-...