论文标题
与Abelian现场对称性的一维间隙相位的分类描述
Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
论文作者
论文摘要
In this work, we analyze the macroscopic observables in the 1+1D gapped phases with Abelian onsite symmetries and show that the spacetime observables for each gapped phase form a clear structure that can be mathematically described by enriched fusion categories, which uncovers the behavior of nonlocal excitations that were blurry in traditional Landau paradigm.这些分类描述不仅为对称性保存和破坏阶段产生已知的分类结果，而且还统一了更广泛的图像中的晶格二元性。在分析了一般晶格模型及其边界之后，我们给出了包括非平凡SPT阶段的明确示例，其中可以通过我们的分类直接给出非平凡边界。使用富集的分类描述，在2D之间的全息二元性下，晶格二元性及其间隙相位。拓扑顺序带有张开的1D边界和1+1D的量子液体，具有分类对称性，该液体阐明了所有量子阶段的统一定义。
In this work, we analyze the macroscopic observables in the 1+1D gapped phases with Abelian onsite symmetries and show that the spacetime observables for each gapped phase form a clear structure that can be mathematically described by enriched fusion categories, which uncovers the behavior of nonlocal excitations that were blurry in traditional Landau paradigm. These categorical descriptions not only generate the known classification results for symmetry preserving and breaking phases, but also unifies lattice dualities in a broader picture. After analyzing the general lattice model together with their boundaries, we give explicit examples including nontrivial SPT phase, where nontrivial boundaries can be given directly through our classification. Using enriched categorical descriptions, the lattice dualities and their gapped phases are unified under a holographic duality between an 2d. topological order with gapped 1d boundaries and 1+1D gapped quantum liquids with a categorical symmetry, which shed light on a unified definition of all quantum phases.
