Efficient flow equations for dissipative systems

Abstract

Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

35 pages plus appendices, 15 figures, comments welcome, Submission to SciPost; added references, added explanations regarding transformations of observables and definitions of $Q$, $H^{+}$ and $H^{-}$, added App. C and App. D containing analytical arguments

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Cited by in corpus (7)

• Many-Body Open Quantum Systems
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Series expansions in closed and open quantum many-body systems with multiple quasiparticle types
• Low-energy spin excitations in field-induced phases of the spin-ladder antiferromagnet BiCu${}_2$PO${}_6$
• Collective modes in superconductors including Coulomb repulsion
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• A method to derive material-specific spin-bath model descriptions of materials displaying prevalent spin physics