论文标题
可逆的亚代代代理
Invertible subalgebras
论文作者
论文摘要
我们在晶格上引入了本地操作员代数的可逆亚代数。可逆的亚代词被定义为一个，使每个本地操作员都可以通过不可允许的亚代词和通勤者的元素在本地表达。在二维晶格上，可逆的亚代词是通过通勤的哈密顿式的授课理论，据信这在任何当地的全部操作员代数上都不可能。我们证明，$ \ mathsf d $二维可逆的亚代词的稳定等效类是张量产品下的Abelian组，与所有$ \ mathsf d + 1 $ dimensional qca Modulo混合等价和移位的组组合。 在附录中，我们考虑了无限晶格的所有QCA组上的一个指标，并证明该指标的完成包含当地哈密顿人的时间演变，这仅是地方性的。我们的度量拓扑严格比强大的拓扑精细。
We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the commutant. On a two-dimensional lattice, an invertible subalgebra hosts a chiral anyon theory by a commuting Hamiltonian, which is believed not to be possible on any full local operator algebra. We prove that the stable equivalence classes of $\mathsf d$-dimensional invertible subalgebras form an abelian group under tensor product, isomorphic to the group of all $\mathsf d + 1$ dimensional QCA modulo blending equivalence and shifts. In an appendix, we consider a metric on the group of all QCA on infinite lattices and prove that the metric completion contains the time evolution by local Hamiltonians, which is only approximately locality-preserving. Our metric topology is strictly finer than the strong topology.
