从迭代(1+1)维规范化的涌现(2+1)维拓扑序
Emergent (2+1)D topological orders from iterative (1+1)D gauging
AI总结：
本文通过迭代规范化自旋链的阿贝尔群对称性并排列规范场，构造出(2+1)维拓扑码，实现任意子禁闭与偶极激发，并自然实现有能隙边界，提供从低维到高维拓扑码的新途径。
摘要：
规范化引入规范场以局域化已有的全局对称性，从而在规范场上产生一个对偶全局对称性，该对称性可再次被规范化。通过在具有阿贝尔群对称性的自旋链上迭代规范化过程，并将规范场排列在二维晶格中，局域对称性成为任意阿贝尔群的$XZZX$码的稳定子。通过扭曲规范化映射，我们获得新码，这些码明确地禁闭任意子，任意子违反奇数个plaquette项，其融合导致可移动偶极激发。我们的构造通过取初始(1+1)维全局对称系统的不同量子相，自然实现任何有能隙边界。我们的方法建立了从低维拓扑码获得高维拓扑码、识别其有能隙边界及其张量网络表示的新途径。
英文摘要：
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group symmetries and arranging the gauge fields in a 2D lattice, the local symmetries become the stabilizer of the $XZZX$-code for any Abelian group. By twisting the gauging map we obtain new codes that explicitly confine anyons, which violate an odd number of plaquette terms and whose fusion results in mobile dipole excitations. Our construction naturally realizes any gapped boundary by taking different quantum phases of the initial (1+1)D globally symmetric system. Our method establishes a new route to obtain higher dimensional topological codes from lower ones, to identify their gapped boundaries and their tensor network representations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
