The weak-coupling CT-QMC approach provides us with an efficient and exible tool to tackle
a number of impurity and lattice problems. In this talk, I will review two extensions of this
algorithm. One is aimed at obtaining ground state properties, projective schemes, and the other
at including phonon-degrees of freedom or more generally retarded interactions. The efficiency
of both extensions will be tested on non-trivial quantum many body problems.
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