Non-Landau quantum phase transition in modulated SU(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>) Heisenberg spin chains

We investigate the nature of the quantum phase transition in modulated $\mathrm{SU}(N)$ Heisenberg spin chains. In the odd-$N$ case, the transition separates a trivial nondegenerate phase to a doubly degenerate gapped chiral $\mathrm{PSU}(N)$ symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the ${\mathbb{Z}}_{2}$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated $\mathrm{SU}(N)$ Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the $\mathrm{SU}{(N)}_{1}$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by slightly changing the model parameters.