Work

Noninvertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry

Year: 2025

Type: article

Abstract: We investigate the interplay between self-duality and spatially modulated symmetry of generalized $N$-state clock models, which include the transverse-field Ising model and ordinary $N$-state clock models as special cases. The spatially modulated symmetry of the model becomes trivial when the model's parameters satisfy a specific number-theoretic relation. We find that the duality is noninvertible when the spatially modulated symmetry remains nontrivial, and we show that this noninvertibility is resolved by introducing a generalized ${\mathbb{Z}}_{N}$ toric code, which manifests ultraviolet/infrared mixing, as the bulk topological order. In this framework, the boundary duality transformation corresponds to the boundary action of a bulk symmetry transformation, with the end point of the bulk symmetry defect realizing the boundary duality defect. Our results illuminate not only a holographic perspective on dualities but also a relationship between spatially modulated symmetry and ultraviolet/infrared mixing in one higher dimension.

Source: Physical review. B./Physical review. B

DOI: 10.1103/physrevb.111.115112

Authors: Donghae Seo, Gil Young Cho, Robert-Jan Slager

Institutions: Pohang University of Science and Technology, Korea Advanced Institute of Science and Technology, Asia Pacific Center for Theoretical Physics, University of Cambridge, University of Manchester

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green