Categorical Symmetries in Spin Models with Atom Arrays

TL;DR

This paper introduces a spin chain model exhibiting categorical symmetries, specifically $ ext{Rep}(D_8)$, to classify phases of matter beyond traditional paradigms, and proposes a practical atomic implementation for simulation.

Contribution

It presents a simple, experimentally feasible spin model that captures all gapped phases and phase transitions governed by categorical symmetries, expanding the understanding of non-invertible phases.

Findings

Model encompasses all gapped phases and second-order phase transitions.

Proposes a practical implementation using neutral atom arrays.

Outlines an efficient digital simulation method for quantum phases.

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.