AGSPs对退化基空间的深刻影响
Sharp implications of AGSPs for degenerate ground spaces
摘要：
我们将[Arad，Landau，and Vazirani '12]的“现成”AGSP $\Rightarrow$纠缠束缚蕴涵从唯一的基态推广到简并的基态空间.我们的条件$RΔ\le1/2$上的$(Δ,R)$-AGSP匹配的非退化的情况下，而现有的工具在文献中的自旋链将只足以证明一个不太自然的暗示，假设$R^{\text{Const}}Δ\le c$。为了表明，$RΔ\le1/2$仍然足以在退化的情况下，我们证明了一个最佳的误差减少界，提高了文献的一个因素$δμ$，其中$δ=1-μ$是可行的。广义off-the-rack界意味着[Anshu，Arad和Gosset '19]的最近的2D子体积定律从非退化情况推广到亚指数退化情况。
英文摘要：
We generalize the `off-the-rack' AGSP$\Rightarrow$entanglement bound implication of [Arad, Landau, and Vazirani '12] from unique ground states to degenerate ground spaces. Our condition $RΔ\le1/2$ on a $(Δ,R)$-AGSP matches the non-degenerate case, whereas existing tools in the literature of spin chains would only be adequate to prove a less natural implication which assumes $R^{\text{Const}}Δ\le c$. To show that $RΔ\le1/2$ still suffices in the degenerate case we prove an optimal error reduction bound which improves on the literature by a factor $δμ$ where $δ=1-μ$ is the viability. The generalized off-the-rack bound implies the generalization of a recent 2D subvolume law of [Anshu, Arad, and Gosset '19] from the non-degenerate case to the sub-exponentially degenerate case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
