Calculating universal properties of quantum phase transitions in microscopic Hamiltonians is a challenging task, made possible through large-scale numerical simulations coupled with finite-size scaling analyses. The continuing advancement of quantum Monte Carlo technologies, together with modern high-performance computing infrastructure, has made amenable a new class of quantum Heisenberg Hamiltonian with four-spin exchange, which may harbor a continuous Néel-to-Valence Bond Solid quantum phase transition. Such an exotic quantum critical point would necessarily lie outside of the standard Landau-Ginzburg-Wilson paradigm, and may contain novel physical phenomena such as emergent topological order and quantum number fractionalization. I will discuss efforts to calculate universal critical exponents using large-scale quantum Monte Carlo simulations, and compare them to theoretical predictions, in particular from the recent theory of deconfined quantum criticality.
