发表机构
Indian Institute of Technology, Bhubaneswar; Stony Brook University（印度技术学院布巴内斯瓦尔分校; 石溪大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分类了有限希尔伯特空间上 Kramers-Wannier 对偶可逆的条件，通过 Ising 键代数表示建立充要判据，并给出非平凡实现中的可逆有序-无序对偶示例。
AI 中文摘要
量子 Ising 链的 Kramers-Wannier 对偶在有限周期链上自然实现为非可逆变换。然而，在纳入适当的对称扭结扇区后，该对偶可提升为可逆的幺正变换。在本文中，我们对 Kramers-Wannier 对偶在有限希尔伯特空间上何时允许可逆实现进行了分类。我们证明这由 Ising 键代数的表示决定，并建立了以其两个中心元素表示的充要条件。这一表示论判据统一了传统的非可逆实现与涉及对称扭结扇区的可逆构造，并同样适用于具有相同底层键代数的其他模型。作为显式示例，我们在 Ising 键代数的一个非平凡实现中发现了一个允许可逆 Kramers-Wannier 对偶的有序-无序对偶。
英文摘要
{\it Kramers-Wannier} duality of the quantum Ising chain is naturally realized as a noninvertible transformation on a finite periodic chain. Upon incorporating appropriate symmetry-twisted sectors, however, the duality can be promoted to an invertible unitary transformation. In this Letter, we classify when the Kramers-Wannier duality admits an invertible realization on a finite Hilbert space. We show that this is determined by the representation of the Ising bond algebra and establish a necessary and sufficient condition in terms of its two central elements. This representation-theoretic criterion unifies the conventional noninvertible realization with invertible constructions involving symmetry-twisted sectors and applies equally to other models with the same underlying bond algebra. As an explicit example, we find an order-disorder duality in a non-trivial realization of the Ising bond algebra that admits an invertible Kramers-Wannier duality.
Comments7 pages; v2 8 pages, added few remarks with updated references
