发表机构
University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于边界态分解的充分条件，证明六角AKLT模型和Ising PEPS具有均匀谱隙，误差随重叠宽度指数衰减。
AI 中文摘要
我们建立了一个充分条件，在该条件下，重叠的PEPS边界态满足谱隙的近似分解准则。该条件以切割矩形区域中心键所诱导的边界响应来表述。我们将该响应分解为与所有四个相关区域共有的贡献，以及以瞬时边界度量测量的余项。一个线性输运吸收了共有贡献，并产生兼容的分解算子，其误差仅由余项控制。我们将此框架应用于Ising PEPS和六角格点上的自旋-3/2 AKLT模型。对于Ising PEPS，所需的边界响应估计简化为Dobrushin-Shlosman型条件。对于六角AKLT模型，路径和环的根展开隔离了共有响应，而边界态的局部比较连同标量Kotecký-Preiss估计控制了剩余项。在两种情况下，分解误差随重叠宽度指数衰减，直至与切割长度成比例的前因子。对于AKLT，我们建立了相应的物理投影算子估计并获得均匀谱隙。对于Ising PEPS，谱隙推论额外要求相容的注入区域收缩，如论文中所指定。更一般地，该方法提供了一条从PEPS边界响应的局域性到二维母哈密顿量谱隙的系统性途径。
英文摘要
We establish a sufficient condition under which overlapping PEPS boundary states satisfy the approximate factorization criterion for a spectral gap. The condition is formulated in terms of the boundary response induced by cutting bonds through the center of a rectangular region. We decompose this response into a contribution common to all four associated regions and a remainder measured in the instantaneous boundary metric. A single linear transport absorbs the common contribution and yields compatible factorization operators, with an error controlled solely by the remainder. We apply this framework to Ising PEPS and to the spin-3/2 AKLT model on the hexagonal lattice. For Ising PEPS, the required boundary-response estimate reduces to a Dobrushin-Shlosman-type condition. For the hexagonal AKLT model, a rooted expansion in paths and loops isolates the common response, while a local comparison of boundary states together with a scalar Kotecký-Preiss estimate controls the remaining terms. In both cases, the factorization error decays exponentially with the overlap width, up to a prefactor proportional to the cut length. For AKLT, we establish the corresponding physical projector estimate and obtain a uniform spectral gap. For Ising PEPS, the gap implication additionally requires compatible injective regional contractions, as specified in the paper. More generally, the method provides a systematic route from locality of PEPS boundary response to spectral gaps of two-dimensional parent Hamiltonians.
