标题： 玻色化和克雷默斯-瓦尼尔对偶性在一般维度中 显示英文标题

标题： Bosonization and Kramers-Wannier dualities in general dimensions

摘要： 众所周知，非相互作用的马约拉纳链通过乔丹-维igner变换或通过规范费米子宇称，与一维横场伊辛模型对偶。在这一对应关系中，马约拉纳链的最小翻译映射到自旋模型的著名克勒默-瓦尼尔（KW）对偶，临界点映射到自对偶点。在本工作中，我们通过构建规范宇称的费米系统与定义在空间任意多面体分解上的自旋系统的单位等价性，将这种映射推广到二维及更高维度。在规范场施加平坦条件的情况下，得到原始（未规范）费米系统与服从高斯定律的规范自旋系统的玻色化对偶。自旋系统中的高斯定律对费米系统中的卡斯特莱恩方向（和离散自旋结构）的依赖关系被明确说明。将这种玻色化应用于平移不变格子上的一个或两个马约拉纳费米子副本，我们推导出自旋系统中由费米最小翻译产生的高维KW（自）对偶性的类比。由于关联对称算子中的高阶对称性本征空间投影，KW（自）对偶性是非可逆的。我们提出的玻色化框架直观、通用且系统，涵盖了其他已知的精确玻色化方法，同时提供了一种新颖的方法，在任意维度中建立费米系统与自旋系统之间的新联系。 显示英文摘要

摘要： It is well known that the noninteracting Majorana chain is dual to the one-dimensional transverse-field Ising model, either through the Jordan-Wigner transformation or by gauging fermion parity. In this correspondence, the minimal translation of the Majorana chain maps to the celebrated Kramers-Wannier (KW) duality of the spin model, with the critical point mapped to the self-dual point. In this work, we generalize this mapping to two and higher dimensions by constructing a unitary equivalence between the parity-gauged fermionic system and a spin system defined on arbitrary polyhedral decompositions of space. Imposing the flatness condition on the gauge field yields a bosonization duality between the original (ungauged) fermionic system and a gauged spin system obeying a Gauss law. The dependence of the Gauss law in the spin system on the Kasteleyn orientation (and the discrete spin structure) of the fermionic system is made explicit. Applying this bosonization to one or two copies of Majorana fermions on translationally invariant lattices, we derive higher-dimensional analogs of KW (self-)dualities in spin systems arising from fermionic minimal translations. The KW (self-)dualities are non-invertible due to projections onto eigenspaces of higher-form symmetries in the associated symmetry operators. The bosonization framework we present is intuitive, general, and systematic, encompassing other known exact bosonization methods while offering a novel approach to establish new connections between fermionic and spin systems in arbitrary dimensions.