发表机构
C. N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, Stony Brook University; Department of Physics, The Pennsylvania State University; Center for Theory of Emergent Quantum Matter, The Pennsylvania State University（石溪大学 C.N. 杨理论物理研究所及物理与天文系; 宾夕法尼亚州立大学物理系; 宾夕法尼亚州立大学涌现量子物质理论中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过全息方法研究基塔耶夫十六重路中费米子退相干，提出三步过程连接二维拓扑序退相干与三维纯态相变，并证明退相干总产生内禀混合态拓扑序。
AI 中文摘要
我们研究二维拓扑序中的任意子退相干，以基塔耶夫十六重路中的费米子退相干作为具体例子。十六重路包含手性拓扑相，这些相被认为不存在可交换投影算子哈密顿量，这使得直接研究其退相干具有挑战性。我们进一步猜想，由这种退相干诱导的相变所产生的密度矩阵可以通过三步过程获得：首先将拓扑序提升到其Walker-Wang模型，然后过渡到另一个Walker-Wang模型，最后对体自由度求迹。这建立了拓扑序的退相干与其三维对应物中的纯态相变之间的联系。我们给出了许多例子。特别地，我们展示了在十六个态中的每一个态中对费米子退相干总是产生一个内禀混合态拓扑序，这是相应三维体总是转变为三维费米子环面码（fTC）这一事实的结果。我们的结果表明了一种在可交换投影算子哈密顿量层面上研究手性拓扑序中任意子退相干的系统方法。
英文摘要
We study anyon decoherence in 2D topological order, with the fermion decoherence in Kitaev's sixteenfold way as explicit examples. The sixteenfold way includes chiral topological phases, which are believed to admit no commuting projector Hamiltonian, making it challenging to study their decoherence directly. We further conjecture the density matrix produced by this decoherence induced phase transition can be obtained by a three-step procedure: first lift the topological order to its Walker-Wang model, followed by a transition to another Walker-Wang model, and finally trace over the bulk degrees of freedom. This establishes a connection between the decoherence of a topological order and a pure state phase transition in its 3D counterpart. Many examples are given. In particular, we show that decohering the fermion in each of the sixteen states always yields an intrinsically mixed-state topological order, a consequence of the fact the corresponding 3D bulk always transits into the 3D fermionic toric code (fTC). Our result suggests a systematic method for studying anyon decoherence in chiral topological orders at the level of commuting projector Hamiltonians.
Comments31 pages, 6 figures, 1 table
