可探测引理和谱隙放大的简单证明
A simple proof of the detectability lemma and spectral gap amplification
摘要：
可探测引理是研究格点自旋模型中无阻挫哈密顿量的带隙基态结构的有效工具。引理提供了一个估计的误差近似的地面空间投影仪与当地的投影仪的产品。我们提供了一个新的，更简单的证明的可检测性引理，它适用于一个任意顺序的本地投影仪，并表明它是紧到一个常数因子。作为一个应用程序，我们展示了如何引理可以与高强逆相结合，以获得局部谱隙放大：我们表明，通过粗粒化一个局部的挫折免费哈密顿与谱隙$γ>0$的长度尺度$O(γ^{-1/2})$，得到一个哈密顿与$Ω(1)$谱隙。
英文摘要：
The detectability lemma is a useful tool for probing the structure of gapped ground states of frustration-free Hamiltonians of lattice spin models. The lemma provides an estimate on the error incurred by approximating the ground space projector with a product of local projectors. We provide a new, simpler proof for the detectability lemma, which applies to an arbitrary ordering of the local projectors, and show that it is tight up to a constant factor. As an application we show how the lemma can be combined with a strong converse by Gao to obtain local spectral gap amplification: we show that by coarse-graining a local frustration-free Hamiltonian with a spectral gap $γ>0$ to a length scale $O(γ^{-1/2})$, one gets an Hamiltonian with an $Ω(1)$ spectral gap.
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。
