Mass generation by fractional instantons in SU($n$) chains

Abstract

Recently, Haldane's conjecture about SU(2) chains has been generalized to SU($n$) chains in the symmetric representations. For a rank-$p$ representation, a gapless phase is predicted when $p$ and $n$ are coprime; otherwise, a finite energy gap is present above the ground state. In this work, we offer an intuitive explanation of this behavior based on fractional topological excitations, which are able to generate a mass gap except when $p$ and $n$ have no common divisor. This is a generalization of an older work in SU(2), which explains the generation of the Haldane gap in terms of merons in the O(3) nonlinear sigma model.

arXiv comment11 pages + 2 pages of appendices

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Cited by in corpus (8)

• Flag manifold sigma models: spin chains and integrable theories
• Haldane Gap of the Three-Box Symmetric $\mathrm{SU}(3)$ Chain
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Strongly coupled QFT dynamics via TQFT coupling
• Flag manifold sigma models from SU($n$) chains
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Edge states and universality class of the critical two-box symmetric SU(3) chain