发表机构
Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart（斯图加特大学理论物理第三研究所与集成量子科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文严格证明了具有$\mathbb{Z}_2$拓扑序的封锁哈密顿量存在有限激发能隙，并推广至非阿贝尔量子双相，利用能隙稳定性与局域对称性完成证明。
AI 中文摘要
在热力学极限下，量子多体系统谱能隙的数学严格证明以困难著称，然而这些证明对于对量子物质相进行分类至关重要。本文中，我们证明了一个特定哈密顿量存在有限激发能隙，该哈密顿量在 [T. F. Maier 等人，PRX Quantum 6, 030340 (2025)] 中提出，并受里德伯平台启发。该哈密顿量仅包含二能级系统之间的两体封锁相互作用，且具有环面码相中的拓扑有序基态。我们证明我们的结果同样适用于更广泛的一类封锁哈密顿量，这类哈密顿量实现非阿贝尔量子双相，并在 [H. P. Büchler 等人，Phys. Rev. B 114, 065113 (2026)] 中提出。该证明基于已知的能隙稳定性结果，并利用了所研究模型的局域对称性。
英文摘要
Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.
Comments44 pages, 5 figures
