Emergent generalized symmetries in ordered phases and applications to quantum disordering

• DOI: 10.21468/scipostphys.17.3.080
• Publication Date: 2024-09-13T14:34:41Z
• Authors: Salvatore D. Pace
• Keywords: High Energy Physics - Theory; Condensed Matter - Strongly Correlated Electrons; Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Physics; QC1-999; FOS: Physical sciences; Mathematical Physics (math-ph); Condensed Matter - Statistical Mechanics; Mathematical Physics

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), absence walls we find symmetry D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math> -dimensional spacetime are described (D-1) display="inline"><mml:mrow><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>D</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo form="postfix">)</mml:mo></mml:mrow></mml:math> -representations a -group depends only on spontaneous symmetry-breaking (SSB) pattern phase. These emergent not spontaneously broken show breaking them induces phase transition into nontrivial disordered can have symmetry-enriched (non-)Abelian topological orders, photons, even more symmetries. This SSB between two distinct phases–an ordinary generalized one–making it possible deconfined quantum critical point. also investigate ’t Hooft anomalies these conjecture there always mixed anomaly microscopic One way this manifest through fractionalization symmetry’s numbers. Our results demonstrate most exotic phases provide valuable framework for characterizing transitions.