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arXiv · 2001.09114

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

Kyle Wamer·Ian Affleck
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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.

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Kyle Wamer, Ian Affleck. 2020-01-24. Mass generation by fractional instantons in SU($n$) chains. https://doi.org/10.1103/physrevb.101.245143

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