标题： 通过希尔伯特空间扩展的不可行性对偶化 显示英文标题

标题： Dualization of ingappabilities through Hilbert-space extensions

摘要： 通过希尔伯特空间扩展方法，可以理解任意维度中的典型对偶性。 通过这些结果，我们严格地将量子禁带转换为一维的离散高度模型，这在以前的工作（如通量插入论证）中是无法实现的。 结果表明，量子离散高度模型的禁带是由一种奇特的“调制”平移对称性所保护的，这种对称性是调制内部对称性变换和传统晶格平移的组合。 它也可以推广到任意维度的高形式规范场，例如二维中的$\mathbb{Z}$规范理论，具有$\mathbb{Z}$一形式对称性和调制平移对称性。 显示英文摘要

摘要： Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by earlier work such as flux-insertion arguments. It turns out that the ingappabilities of quantum discrete height model is protected by an exotic "modulating" translation symmetry, which is a combination of modulating internal symmetry transformation and the conventional lattice translation. It can be also generalize to higher-form gauge fields in arbitrary dimensions, e.g., $\mathbb{Z}$-gauge theory in two dimensions with $\mathbb{Z}$ one-form symmetry and a modulating translation symmetry.