Mass generation by fractional instantons in SU( n ) chains

Abstract

Recently, Haldane's conjecture about SU(2) chains has been generalized to $\mathrm{SU}(n)$ 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 $\ensuremath{\sigma}$ model.