A Tensor Network Framework for Lindbladian Spectra and Steady States

Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Akin to the equilibrium case, this requires the computation of the low-lying eigenstates of Lindbladians, a problem challenging conventional approaches for simulating quantum many-body systems. In this talk, I will introduce a tensor-network based framework to systematically compute not only steady states, but also low-lying excited states with unprecedented precision for large driven quantum many-body systems. The framework is based on recent advances utilizing complex-time Krylov spaces, and we leverage these ideas to create a toolbox tailored to solve the challenging non-Hermitian eigenvalue problem ubiquitous in open quantum systems.