Adapted continuous unitary transformation to treat systems with quasi-particles of finite lifetime

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasi-particles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder, which allows for spontaneous triplon decay. We present results for the low-energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.