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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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.
Kaul, Ribku K., "Marshall-Positive SU(N) Quantum Spin Systems and Classical Loop Models: A Practical Strategy to Design Sign-Problem-Free Spin Hamiltonians" (2015). Physics and Astronomy Faculty Publications. 289.