Categorical Symmetries in Spin Models with Atom Arrays

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• High Energy Physics

Background:

• Categorical symmetries offer a generalized framework for classifying phases of matter, extending the traditional Landau theory.
• Non-invertible phases and their associated symmetries represent a frontier in condensed matter physics, demanding new theoretical and experimental tools.

Purpose of the Study:

• To propose and analyze a simple spin chain model that captures all gapped phases and second-order phase transitions governed by the Rep(D8) categorical symmetry.
• To demonstrate the practical feasibility of realizing and simulating such models using current experimental techniques.

Main Methods:

• Development of a spin chain model incorporating Rep(D8) categorical symmetry.
• Proposal for experimental implementation using neutral atoms in optical tweezer arrays.
• Utilizing a dual-species setup and Rydberg blockade for digital quantum simulation.

Main Results:

• The proposed model successfully encompasses gapped phases and second-order phase transitions associated with Rep(D8) symmetry.
• The digital simulation approach enables efficient exploration of many-body evolution in nontrivial quantum phases.
• The model's simplicity facilitates practical realization and experimental testing of categorical symmetry predictions.

Conclusions:

• The Rep(D8) spin chain model provides a tractable platform for studying generalized phases of matter.
• Neutral atom quantum simulation offers a promising avenue for experimentally investigating non-invertible phases and categorical symmetries.
• This work bridges theoretical advancements in categorical symmetry with concrete experimental proposals in quantum simulation.