Paper published in Physical Review Letters on noninvertible symmetry-protected topological phases

Postdoc Weiguang Cao has together with Masahito Yamazaki from Kavli Institute for the Physics and Mathematics of the Universe at University of Tokyo, and Linhao Li from University of Ghent (now moved to the Pennsylvania State University) published results in Physical Review Letters, accepted on 15^th of December 2025, in a paper entitled: “Duality viewpoint of noninvertible symmetry-protected topological phases”.

In their work, the authors explore recent developments in generalized symmetries, focusing especially on gapped phases of matter that exhibit noninvertible symmetries - a class of symmetries that have attracted significant interest due to their fundamentally novel behaviour compared to conventional group symmetries. Through the use of duality transformations, they show how the classification and construction of gapped phases with noninvertible symmetry can be systematically mapped to more familiar frameworks involving standard group symmetries.

The article provides a broad classification of symmetry-protected topological phases featuring these noninvertible symmetries across arbitrary spacetime dimensions, revealing new structures and classifications that go beyond those associated with traditional symmetry groups. Furthermore, the authors build lattice models in both (1+1)-dimensional and (2+1)-dimensional settings that realize these newly identified phases and investigate the nature of their anomalous interfaces.

This duality-based viewpoint offers a powerful conceptual and technical bridge between conventional symmetry-based classifications and the rapidly expanding landscape of generalized, including noninvertible, symmetries in modern condensed matter physics.

Link to the abstract of the accepted paper here.