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An improved generator for continuous unitary transformations is introduced todescribe systems with unstable quasiparticles. Its general properties arederived and discussed. To illustrate this approach we investigate theasymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows forspontaneous triplon decay. We present results for the low energy spectrum andthe momentum resolved spectral density of this system. In particular, we showthe resonance behavior of the decaying triplon explicitly.

Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime