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We discuss designer Hamiltonians---lattice models tailored to be free fromsign problems ("de-signed") when simulated with quantum Monte Carlo methods butwhich still host complex many-body states and quantum phase transitions ofinterest in condensed matter physics. We focus on quantum spin systems in whichcompeting interactions lead to non-magnetic ground states. These states and theassociated quantum phase transitions can be studied in great detail, enablingdirect access to universal properties and connections with low-energy effectivequantum field theories. As specific examples, we discuss the transition from aNeel antiferromagnet to either a uniform quantum paramagnet or a spontaneouslysymmetry-broken valence-bond solid in SU(2) and SU(N) invariant spin models. Wealso discuss anisotropic (XXZ) systems harboring topological Z2 spin liquidsand the XY* transition. We briefly review recent progress on quantum MonteCarlo algorithms, including ground state projection in the valence-bond basisand direct computation of the Renyi variants of the entanglement entropy.

Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations