AI 中文总结
该研究在子区域复杂度-体积猜想下，对比非平衡Stückelberg全息超导体的HSC与HEE，发现HEE更鲁棒，HSC依赖子系统大小。
AI 中文摘要
在子区域复杂度-体积猜想框架下，我们针对非平衡Stückelberg全息超导体中的条带结构，数值对比了全息子区域复杂度（HSC）与全息纠缠熵（HEE）。改变Stückelberg参数γ会引发二级和一级相变，两种可观测量均可指示这些相变，但鲁棒性存在显著差异。HEE的定性特征在所有条带宽度下均保持，且超导相中HEE的有限部分始终小于正常相。HSC则强烈依赖条带宽度：在小条带宽度ℓ时，其温度演化趋势与HEE相反；在大ℓ时则与HEE一致。因此，超导相与正常相的HSC分支相对排序发生反转，形成两者近乎重合的交叉区域，此时仅靠HSC无法可靠判定相变是否发生或其阶数，需从巨正则势中选取物理分支。综上，HEE是更鲁棒的诊断工具，而HSC是尺度依赖的探针，其解释明确依赖子系统大小。
英文摘要
Within the subregion complexity-volume conjecture, we numerically compare holographic subregion complexity (HSC) and holographic entanglement entropy (HEE) for a strip in unbalanced Stückelberg holographic superconductors. Varying the Stückelberg parameter $γ$ yields both second- and first-order transitions. Both observables signal these transitions, but with markedly different robustness. The qualitative HEE signatures persist across strip widths, and the finite part of HEE remains smaller in the superconducting phase than in the normal phase. The HSC is instead strongly width dependent: its temperature trend is opposite to that of HEE at small $\ell$ and agrees with it at large $\ell$. Consequently, the superconducting and normal HSC branches reverse their relative ordering, creating a crossover region where they nearly coincide. There, HSC alone cannot reliably determine the occurrence or order of the transition, and the physical branch must be selected from the grand potential. Thus, HEE provides a more robust diagnostic, whereas HSC is a scale-dependent probe whose interpretation depends explicitly on the subsystem size.
Comments19 pages, 16 figures
