标题： 全息对应于体边界局部拓扑序 显示英文标题

标题： Holography for bulk-boundary local topological order

摘要： 在我们之前的论文[arXiv:2307.12552]中，我们为量子自旋系统引入了局部拓扑序（LTO）公理，这使我们能够定义一个由低一维的边界代数网络表现的物理边界。 这为拓扑全息提供了形式化的设定，在其中，物理边界代数的DHR双模的编织张量范畴捕捉了体的拓扑序。 在本文中，我们将LTO公理扩展到配备有拓扑边界的量子自旋系统，再次为体-边界系统生成一个物理边界代数，其（拓扑）边界DHR双模的范畴恢复了拓扑边界序。 我们对Levin-Wen和Walker-Wang体-边界系统进行了详细的分析。 在此过程中，我们引入了一个由单位编织融合范畴（UBFC）构建的二维编织范畴代数网。 这样的网作为Walker-Wang模型的边界代数出现。 我们考虑了对应于Walker-Wang模型标准拓扑边界的该编织范畴代数上的规范态。 有趣的是，在这种状态下，锥形冯诺依曼代数是I型且中心是有限维的，与我们在[arXiv:2307.12552]中研究的Levin-Wen模型中的II型和III型锥形冯诺依曼代数形成对比。 它们的守恒子域恢复了我们UBFC的基础单位范畴，我们猜想守恒子域范畴也捕捉了融合和编织。 显示英文摘要

摘要： In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary manifested by a net of boundary algebras in one dimension lower. This gives a formal setting for topological holography, where the braided tensor category of DHR bimodules of the physical boundary algebra captures the bulk topological order. In this article, we extend the LTO axioms to quantum spin systems equipped with a topological boundary, again producing a physical boundary algebra for the bulk-boundary system, whose category of (topological) boundary DHR bimodules recovers the topological boundary order. We perform this analysis in explicit detail for Levin-Wen and Walker-Wang bulk-boundary systems. Along the way, we introduce a 2D braided categorical net of algebras built from a unitary braided fusion category (UBFC). Such nets arise as boundary algebras of Walker-Wang models. We consider the canonical state on this braided categorical net corresponding to the standard topological boundary for the Walker-Wang model. Interestingly, in this state, the cone von Neumann algebras are type I with finite dimensional centers, in contrast with the type II and III cone von Neumann algebras from the Levin-Wen models studied in [arXiv:2307.12552]. Their superselection sectors recover the underlying unitary category of our UBFC, and we conjecture the superselection category also captures the fusion and braiding.