将自旋反铁磁体基态相变问题转化为图论中的加权最大割难题。
Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets
- 用加权图表示希尔伯特空间，波函数符号重构等价于加权最大割。
- 证明该问题在最坏情况下属于NP难，计算复杂度高。
- 为量子多体系统相变分析提供了组合优化新视角，适合量子计算与复杂性研究者。
我们研究了海森堡反铁磁体基态相结构的学习计算复杂度。将希尔伯特空间表示为加权图，变分能量定义了一个加权XY模型，对于ℤ₂对称相，该模型退化为图上的经典反铁磁伊辛模型。当振幅固定时，基态波函数符号的重构等价于一个加权最大割（Max-Cut）实例。这表明海森堡反铁磁体基态相重构在最坏情况下是NP难的，将该任务与组合优化联系起来。
原文摘要 · Abstract (English)
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.
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