We study the fracton phase described by the Chamon model in a manifold with a boundary. The new processess and excitations emerging at the boundary can be understood by means of a diagrammatic framework. From a continuum perspective, the boundary theory is described by a set of scalar fields in similarity with standard $K$-matrix Chern-Simons theory. The continuum theory recovers the gapped boundaries of the lattice model once we include sufficiently strong interactions that break charge conservation. The analysis of the perturbative relevance of the leading interactions reveals a regime in which the Chamon model can have a stable gapless fractonic phase at its boundary.
• Corrected the typos pointed out by Referee 1.
• Modified Fig. 2 to highlight the sites where the spin operators are applied.
• Updated Refs. [30,32,43,53,56,59], which are now published.
• Added citations to J. Sous and M. Pretko, npj Quantum Materials (2020); J. Sous and M. Pretko, Phys. Rev. B 102, 214437 (2020); W. Shirley, X. Liu and A. Dua, Phys. Rev. B 107(3) (2023); R. M. Nandkishore and M. Hermele, Annu. Rev. Condens. Matt. Phys. 10, 295 (2019); M. Pretko, X. Chen and Y. You, Int. J. Mod. Phys. A 35, 2030003 (2020); S. Liu and W. Ji, Towards Non-Invertible Anomalies from Generalized Ising Models, arXiv: 2208.09101 (2022).
• Expanded to introduction to elaborate on the comparison with related models and emphasize our main results.
• Included the factor of as in the lattice vectors above Eq. (1).
• Added a discussion about the ground state degeneracy below Eq. (3).
• Added an explanation about the nomenclature of multipoles on page 5.
• Included the definition of boundary fracton and further discussion about the boundary stabilizers below Eq. (6).
• Corrected factors of 2 in Eqs. (57), (58), and (71); these factors do not affect our conclusions.
• Rewrote Eq. (76) to give a more general expression for the exponents for cosine operators
with non-elementary charges.
• On page 18, expanded the discussion about the gapless boundary phase.
• On page 19, added remarks about the comparison with the X-cube model.
