Emergent SU(N) symmetry in disordered SO(N) magnetic chains

We show that strongly disordered magnetic chains invariant under the SO(N) group display antiferromagnetic
phases with emergent SU(N) symmetry. At zero-temperature, the phases with SU(N) emergent symmetry
develop in two different types of ground states, formed either of randomly distributed singlets of strongly bound couples of SO(N) spins (mesonic phase), or composed of singlets made out of strongly bound integer multiples of N-tuples of
spins (baryonic phase). Both phases display low-temperature excitations behaving as quarks of SU(N).
Amongst the SO(N) symmetric spin chains, we argue that the cases with N = 2, 3, 4 and 6 represent
promising candidates to realize these phases in already well-established scenarios. Our mechanism,
nevertheless, is general, depleting all possible phases of disordered chains with SO(N) symmetry in
its defining representation. The generality of our results settles them as a building block towards a
general understanding of symmetry emergence in disordered many-body problems.