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In this paper, we investigate topological properties of the ground state ofthe SU(N) Heisenberg chain, which is argued to be relevant to theMott-insulating phase of alkaline-earth cold fermions in a one-dimensionaloptical lattice. By calculating the entanglement spectrum, we show that theground state is in one of the topological phases protected by SU(N) symmetry.We then discuss an alternative characterization of it with non-local stringorder parameters. We also consider how the reduction of the protecting symmetryaffects the topological phase paying particular attention to the entanglementspectrum.

Symmetry-protected topological order in SU(N) Heisenberg magnets --quantum entanglement and non-local order parameters