Topological liquids and valence cluster states in two-dimensional SU(N) magnets

Abstract

We study the zero temperature phase diagram of a class of two-dimensional SU(N) antiferromagnets. These models are characterized by having the same type of SU(N) spin placed at each site of the lattice, and share the property that, in general, more than two spins must be combined to form a singlet. An important motivation to study these systems is that they may be realized naturally in Mott insulators of alkaline earth atoms placed on optical lattices; indeed, such Mott insulators have already been obtained experimentally, although the temperatures are still high compared to the magnetic exchange energy. We study these antiferromagnets in a large-N limit, finding a variety of ground states. Some of the models studied here have a valence bond solid ground state, as was found in prior studies, yet we find that many others have a richer variety of ground states. Focusing on the two-dimensional square lattice, in addition to valence cluster states (which are analogous to valence bond states), we find both Abelian and non-Abelian chiral spin liquid ground states, which are magnetic counterparts of the fractional quantum Hall effect. We also find a "doubled" chiral spin liquid ground state that preserves time reversal symmetry. These results are based on a combination of rigorous lower bounds on the large-N ground state energy, and a systematic numerical ground state search. We conclude by discussing whether experimentally relevant SU(N) antiferromagnets -- away from the large-N limit -- may be chiral spin liquids.

26 pages, 7 figures. Very minor changes from v1. Typos corrected in v3

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• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Magnetic crystals and helical liquids in alkaline-earth fermionic gases
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• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
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• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
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