  Reliable simulations of correlated quantum systems, including
high-temperature superconductors and frustrated magnets, are increasingly
desired nowadays to further understanding of essential features in such
systems. Quantum Monte Carlo (QMC) is a unique numerically-exact and
intrinsically-unbiased method to simulate interacting quantum many-body
systems. More importantly, when QMC simulations are free from the notorious
fermion-sign problem, they can reliably simulate interacting quantum models
with large system size and low temperature to reveal low-energy physics such as
spontaneously-broken symmetries and universal quantum critical behaviors. Here,
we concisely review recent progresses made in developing new sign-problem-free
QMC algorithms, including those employing Majorana representation and those
utilizing hot-spot physics. We also discuss applications of these novel
sign-problem-free QMC algorithms in simulations of various interesting quantum
many-body models. Finally, we discuss possible future directions of designing
sign-problem-free QMC methods.
