Categorical Landau Paradigm for Gapped Phases

We propose a unified framework to classify gapped infrared phases with categorical symmetries, leading to a generalized, categorical Landau paradigm. This is applicable in any dimension and gives a succinct, comprehensive, and computationally powerful approach to classifying gapped symmetric phases. The key tool is the symmetry topological field theory, which is a one dimension higher topological field theory with two boundaries that we choose to be topological. We illustrate the general idea for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo><a:mtext>D</a:mtext></a:mrow></a:math> gapped phases with categorical symmetries and suggest higher-dimensional extensions. Published by the American Physical Society 2024