Categorical Symmetries in Spin Models with Atom Arrays

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:mi mathvariant="sans-serif">Rep</a:mi> </a:mrow> <a:mo stretchy="false">(</a:mo> <a:msub> <a:mrow> <a:mi>D</a:mi> </a:mrow> <a:mrow> <a:mn>8</a:mn> </a:mrow> </a:msub> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> . This model not only captures the essential features of noninvertible 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.