Revision 1

Accepted · first revision · record

Title: Classification of intrinsically gapless topological phases
Plain: Some gapless (critical) states carry protected edge modes that no gapped phase with the same symmetry can have, and a general list of such gapless topological phases is missing.
Precise: Classify symmetry-enriched gapless phases of 1D and 2D lattice models, including gapless SPT and intrinsically gapless SPT phases defined by an emergent anomaly in the low-energy symmetry action, and determine which carry protected edge modes. An answer is a classification in terms of symmetry extensions and anomalies with a lattice example in each class.
Settled by: A classification scheme in terms of symmetry extensions and anomalies, verified by explicit lattice realizations of every class in 1D and 2D.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: Gapless SPT phases were introduced in 1D (Scaffidi, Parker, Vasseur 2017), extended to intrinsically gapless SPT (Thorngren, Vishwanath, Verresen 2021) and classified in 1+1D by topological holography (Wen and Potter 2023); a general 2D classification is open as of 2026.
Posed since: 2017