通量条件Kitaev模型中环面码vison晶体的精确选择
Exact selection of a toric-code vison crystal in a flux-conditioned Kitaev model
- School of Physics, Hangzhou Normal University（杭州师范大学物理学院）
- School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）
- Lanzhou Center for Theoretical Physics, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University（兰州大学理论物理中心，教育部量子理论与应用重点实验室，甘肃省量子物理基础学科研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究构造精确可解的Kitaev模型扩展，通量决定马约拉纳跳跃连通性，精确选择2/3-vison晶体作为基态，实现非微扰规范-物质反馈与拓扑简并。
AI中文摘要：
我们构造了自旋$1/2$ Kitaev蜂窝模型的精确可解扩展，其中守恒的$\mathbb{Z}_2$通量不仅决定最近邻马约拉纳跳跃的符号，还决定其连通性。在调谐的环点处，跳跃仅存在于相反通量斑块之间，因此每个顶点的活跃度为0或2，物质哈密顿量在每个通量扇区中分解为独立的马约拉纳环和孤立的零模。精确的环谱和键计数随后在所有局部通量构型和所有四个Wilson环扇区上界定了物质能量，并将其精确分解为受挫三角晶格伊辛项（其广泛简并的基态是完全填充的环覆盖）和非负的马约拉纳残差。在可容许的共度环面上，残差精确选择三个平移相关的$2/3$-vison晶体，它们饱和该界限，并且精确的费米子宇称恒等式表明，对于反铁磁耦合，它们的真空态也经受住投影，使其成为自旋模型的严格基态。在单个晶体内，深度为一的局部幺正变换将基态空间映射到剪切方形晶格环面码的基态空间，给出四重拓扑简并。该模型因此实现了精确的非微扰规范-物质反馈：通量固定了马约拉纳费米子可以移动的位置，而它们的零点能反过来选择具有自发破缺平移对称性的拓扑有序vison晶体。
英文摘要：
We construct an exactly solvable extension of the spin-$1/2$ Kitaev honeycomb model in which conserved $\mathbb{Z}_2$ fluxes determine not only the signs but also the connectivity of nearest-neighbor Majorana hopping. At a tuned loop point, hopping survives only across opposite-flux plaquettes, so every vertex has active degree zero or two and the matter Hamiltonian fragments in each flux sector into independent Majorana rings and isolated zero modes. Exact ring spectra and bond counting then bound the matter energy over all local flux configurations and all four Wilson-loop sectors, and split it exactly into a frustrated triangular-lattice Ising term, whose extensively degenerate ground states are the fully packed loop coverings, and a non-negative Majorana residual. On admissible commensurate tori, the residual selects precisely the three translation-related $2/3$-vison crystals, which saturate the bound, and an exact fermion-parity identity shows that for antiferromagnetic coupling their vacua also survive projection, making them rigorous ground states of the spin model. Within a single crystal, a depth-one local unitary then maps the ground space onto that of a sheared square-lattice toric code, giving fourfold topological degeneracy. The model thus realizes exact nonperturbative gauge-matter feedback: the flux fixes where the Majorana fermions may move, and their zero-point energy selects in return a topologically ordered vison crystal with spontaneously broken translation symmetry.
