Flag manifold sigma models from SU(n) chains
Abstract
One dimensional SU(n) chains with the same irreducible representation R at each site are considered. We determine which R admit lowenergy mappings to a SU (n) /^{[U (1) ] n  1} flag manifold sigma model, and calculate the topological angles for such theories. Generically, these models will have fields with both linear and quadratic dispersion relations; for each R, we determine how many fields of each dispersion type there are. Finally, for purely linearlydispersing theories, we list the irreps that also possess a Z_{n} symmetry that acts transitively on the SU (n) /^{[U (1) ] n  1} fields. Such SU(n) chains have an 't Hooft anomaly in certain cases, allowing for a generalisation of Haldane's conjecture to these novel representations. In particular, for even n and for representations whose Young tableaux have two rows, of lengths p_{1} and p_{2} satisfying p_{1} ≠p_{2}, we predict a gapless ground state when p_{1} +p_{2} is coprime with n. Otherwise, we predict a gapped ground state that necessarily has spontaneously broken symmetry if p_{1} +p_{2} is not a multiple of n.
 Publication:

Nuclear Physics B
 Pub Date:
 October 2020
 DOI:
 10.1016/j.nuclphysb.2020.115156
 arXiv:
 arXiv:2007.01912
 Bibcode:
 2020NuPhB.95915156W
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 26 pages + 9 pages of appendices