In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(105) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions - a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the "designer" Hamiltonians.

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Published in Journal of Physics: Conference Series, v. 640, conference 1, 012041, p. 1-9.

Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd.

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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The authors would like to acknowledge Jon D’Emidio, Roger Melko, and Anders Sandvik for collaboration on related work and NSF DMR-1056536 for partial financial support.

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This paper was presented at the XXVI IUPAP Conference on Computational Physics (CCP2014), August 11-14, 2014, in Boston, MA. For more papers and information from this conference, please visit: http://iopscience.iop.org/issue/1742-6596/640/1