Meron-Cluster Solution of Fermion and Other Sign Problems

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Important examples include QCD and other field theories at non-zero chemical potential, at non-zero vacuum angle, or with an odd number of flavors, as well as the Hubbard model for high-temperature superconductivity and quantum antiferromagnets in an external magnetic field. In all these cases standard simulation algorithms require an exponentially large statistics in large space-time volumes and are thus impossible to use in practice. Meron-cluster algorithms realize a general strategy to solve severe sign problems but must be constructed for each individual case. They lead to a complete solution of the sign problem in several of the above cases.