Quantum Monte Carlo simulations of fermions suffer from the notorious sign problem which is exponentially severe in the volume and in the inverse temperature of the system. Similar problems related to a complex action arise in quantum field theories at non-zero chemical potential or at non-zero theta-vacuum angle. The meron-cluster algorithm identifies groups of canceling configurations and samples only the remaining uncanceled ones. Although this method is not generally applicable, meron-cluster algorithms have been used to completely solve a number of very severe sign problems involving fermions, chemical potential, and theta-vacua. Unfortunately, the meron-cluster algorithm does not solve the sign problem in frustrated quantum spin systems. Still, a nested cluster algorithm allows us to solve this problem for arbitrarily large volumes, at least at moderate temperatures.
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