The established approach of perturbative continuous unitary transformations (pCUTs) constructs effective quantum many-body Hamiltonians as perturbative series that conserve the number of one quasiparticle type. We extend the pCUT method to similarity transformations—dubbed ${\text{pcst}}^{++}$—allowing for multiple quasiparticle types with complex-valued energies. This enlarges the field of application to closed and open quantum many-body systems with unperturbed operators corresponding to arbitrary superimposed ladder spectra. To this end, a generalized counting operator is combined with the quasiparticle generator for open quantum systems recently introduced by Schmiedinghoff and Uhrig [G. Schmiedinghoff and G. S. Uhrig, SciPost Phys. 13, 122 (2022)]. The ${\text{pcst}}^{++}$ then yields model-independent block-diagonal effective Hamiltonians and Lindbladians, allowing a linked-cluster expansion in the thermodynamic limit similar to the conventional pCUT method. We illustrate the application of the ${\text{pcst}}^{++}$ method by discussing representative closed, open, and non-Hermitian quantum systems.

• Received 6 February 2023
• Accepted 21 June 2023

DOI:https://doi.org/10.1103/PhysRevA.108.013323