A research group consisting of Dr. Weiguang Cao (University of Southern Denmark), Prof. Masahito Yamazaki (Department of Physics, Graduate School of Science, The University of Tokyo, and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI)), and Dr. Linhao Li (Ghent University at the time of publication; currently at Pennsylvania State University) has succeeded in establishing a systematic classification and construction of symmetry-protected topological (SPT) phases protected by non-invertible symmetries, by employing a powerful theoretical framework known as duality.

In this study, the authors demonstrate that, through duality transformations, the challenging problem of SPT phases with non-invertible symmetries can be mapped onto the well-understood problem of phases with spontaneous symmetry breaking (SSB), which can be analyzed using existing theoretical tools. This approach enables the classification of SPT phases protected by non-invertible symmetries in arbitrary spacetime dimensions, and furthermore allows for the explicit construction of concrete models realizing such phases.

Compared with previous studies, this work has two major novel aspects: first, it provides an intuitive understanding of the complex structure of non-invertible symmetries using the familiar language of conventional physics; and second, it presents a general classification applicable to arbitrary dimensions. These results are expected to contribute to the exploration of new quantum phases and to the identification of novel resources for quantum computation.

See below for more information.

• Yamazaki Group：https://member.ipmu.jp/masahito.yamazaki/index-j.shtml
• UTokyo FOCUS：https://www.s.u-tokyo.ac.jp/en/press/11057/
• Aritcle URL：https://doi.org/10.1103/4zfz-x9xh