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arXiv · 2302.01000

Series expansions in closed and open quantum many-body systems with multiple quasiparticle types

L. Lenke·A. Schellenberger·K. P. Schmidt
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Abstract

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 $\mathrm{pcst}^{\texttt{++}}$ - 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 (arXiv:2203.15532). The $\mathrm{pcst}^{\texttt{++}}$ 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 $\mathrm{pcst}^{\texttt{++}}$ method by discussing representative closed, open, and non-Hermitian quantum systems.

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L. Lenke, A. Schellenberger, K. P. Schmidt. 2023-02-02. Series expansions in closed and open quantum many-body systems with multiple quasiparticle types. https://doi.org/10.1103/physreva.108.013323

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