We consider bipartite SU(N) spin Hamiltonians with a fundamental representation on one sublattice and a conjugate to fundamental on the other sublattice. By mapping these antiferromagnets to certain classical loop models in one higher dimension, we provide a practical strategy to write down a large family of SU(N) symmetric spin Hamiltonians that satisfy Marshall's sign condition. This family includes all previously known sign-free SU(N) spin models in this representation and in addition provides a large set of new models that are Marshall positive and can hence be studied efficiently with quantum Monte Carlo methods. As an application of our idea to the square lattice, we show that in addition to Sandvik's Q term, there is an independent nontrivial four-spin R term that is sign free. Using numerical simulations, we show how the R term provides a new route to the study of quantum criticality of Néel order.

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Published in Physical Review B: Condensed Matter and Materials Physics, v. 91, no. 5, article 054413, p. 1-7.

©2015 American Physical Society

The copyright holder has granted permission for posting the article here.

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The author thanks K. Damle, T. C. Lang, M. A. Levin, and A. W. Sandvik for stimulating discussions, J. Demidio for his help in preparing some figures, NSF Grant No. DMR-1056536 for partial financial support, and the visitor programs at BU for their hospitality during the preparation of this manuscript. Part of this work was completed while the author held an adjunct faculty position at the TIFR.

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