I will talk about two recent surprises in the simulation of quantum phase transitions. 

Surprise one is the solution of a thirty years old sign problem by the continuous-time QMC approach and the Majorana fermion representation. Practically, it enables us to study several unconventional quantum critical points unbiasedly to high precision. Conceptually, the attempts to unify the two solutions deepen our understanding of the sign problem and provide a new guideline for sign-problem-free QMC simulation of correlated fermions. 

Surprise two is a generic, efficient and elegant approach to compute fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in modern QMC methods. It can be used to detect quantum phase transitions without any prior knowledge of the local order parameter. Using it I will shed light on the hypothetical spin-liquid phase in the Hubbard model on honeycomb lattice.

I will address the relevance of these developments to ultracold atom experiments throughout the talk.