论文标题
AGSP对退化地面空间的急剧影响
Sharp implications of AGSPs for degenerate ground spaces
论文作者
论文摘要
我们将[Arad，Landau和Vazirani '12]从独特的地面状态到堕落的地面空间的[Arad，Landau和Vazirani '12]概括为“无关”的AGSP $ \ rightarrow $纠缠约束。我们的条件$rδ\ le1/2 $在$（δ，r）$ - AGSP符合非脱位案例，而旋转链文献中现有的工具只有足以证明$ r^{\ text} {const}}}δ\ le c $的自然含义。为了表明$rδ\ le1/2 $在退化情况下仍然足够，我们证明了最佳的误差减少结合，该结合通过$δμ$ $δ= 1-μ$的因子$δμ$改善文献是可行性。广义的离线结合意味着[ANSHU，ARAD和GOSSET '19]的最新2D亚量法的概括从非分级案例到亚指数变性案例。
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.
