arXiv cs.AI· Mahmud Ashraf Shamim, Md Moshiur Rahman Raj, Mohamed Hibat-Allah, Paulo T Araujo·· 13 小时前AI 评分15
海森堡反铁磁体变分波函数相位优化复杂度的图论分析
Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets
AI 导读
研究将海森堡反铁磁体基态相位结构的学习问题转化为图论问题：把希尔伯特空间表示为加权图后，变分能量对应加权 XY 模型，在 Z₂ 相位下退化为经典反铁磁 Ising 模型；固定振幅时，重构基态波函数符号等价于加权 Max-Cut 实例，从而将波函数符号优化与组合优化直接关联。作者已更正原文的 NP-hardness 表述，并修订了与变分蒙特卡洛的关联部分。
正文 · 原文
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 links sign optimization of wavefunctions directly to combinatorial optimization.
| Comments: | The NP-hardness claim has been corrected, and the connection to variational Monte Carlo has been revised |
| 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:2602.04943v4 [cond-mat.str-el] for this version) | |
| https://doi.org/10.48550/arXiv.2602.04943 arXiv-issued DOI via DataCite |
Submission history
From: Mahmud Shamim [view email]
[v1]
Wed, 4 Feb 2026 18:53:18 UTC (111 KB)
[v2]
Mon, 9 Feb 2026 17:40:42 UTC (485 KB)
[v3]
Tue, 7 Apr 2026 17:08:16 UTC (507 KB)
[v4]
Mon, 19 Oct 2026 19:28:06 UTC (507 KB)
来源：arXiv cs.AI · arxiv.org