无限量子自旋系统中的拓扑有序态
Topologically ordered states in infinite quantum spin systems
摘要：
本文讨论了无限量子自旋系统中拓扑有序态的一些性质。我们首先研究Kitaev的阿贝尔量子双模型的无限体积基态的集合。我们表明，描述一个单一的激发在散装的状态是无限体积基态，也就是说，局部扰动不能删除的电荷。单激发态对不同电荷是不等价的，它给出了基态集合的扇形理论的完整表征。此外，任何纯基态都等价于某个单激发基态。我们继续研究的稳定性的收费，是由某些代表性的代数可观的分类。我们引入了一个新的超选择准则，选择几乎定域的和可输的$*$ -自同态关于一个真空态。满足超选择准则的表示的等价类形成系统的不同带电超选择扇区。我们证明了如果真空态满足一定的定域性条件，那么超选择结构将是一个辫状张量$C^*$范畴。此外，这种超选择结构是稳定的变形的准局部动力学。这一结果表明阿贝尔量子双模型的任意子结构在局域扰动下是稳定的。
英文摘要：
This dissertation discusses some properties of topologically ordered states as they appear in the setting of infinite quantum spin systems. We begin by studying the set of infinite volume ground states for Kitaev's abelian quantum double models. We show that states describing a single excitation in the bulk are infinite volume ground states, that is, local perturbations cannot remove the charge. The single excitations states, which are inequivalent for distinct charges, give a complete characterization of the sector theory for the set of ground states. Furthermore, any pure ground state is equivalent to some single excitation ground state. We proceed to study the stability of charges that are classified by certain representations of the algebra of observables. We introduce a new superselection criterion selecting almost localized and transportable $*$-endomorphisms with respect to a vacuum state. Equivalence classes of representations satisfying the superselection criterion form different charged superselection sectors of the system. We show that if the vacuum state satisfies certain locality conditions then the superselection structure will be a braided tensor $C^*$-category. Further, this superselection structure is stable up to deformations by a quasi-local dynamics. This result is then applied to show that the anyon structure of the abelian quantum double models is stable under local perturbations.
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。
