Categorical Symmetries in Spin Models with Atom Arrays

Abstract

Categorical symmetries have recently been shown to generalize the classification of phases of matter, significantly broadening the traditional Landau paradigm. To test these predictions, we propose a simple spin chain model that encompasses all gapped phases and second-order phase transitions governed by the categorical symmetry $\mathsf{Rep}(D_8)$. This model not only captures the essential features of non-invertible phases but is also straightforward enough to enable practical realization. Specifically, we outline an implementation using neutral atoms trapped in optical tweezer arrays. Employing a dual-species setup and Rydberg blockade, we propose a digital simulation approach that can efficiently implement the many-body evolution in several nontrivial quantum phases.

4 pages + appendices, v2: added numerical analysis and discussion of intrinsically gapless SSB phase, v3: published in PRL

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• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains