A Tensor Network Framework for Lindbladian Spectra and Steady States

• URL: http://arxiv.org/abs/2509.07709v1
• Date: Tue, 09 Sep 2025 13:12:16 GMT
• Title: A Tensor Network Framework for Lindbladian Spectra and Steady States
• Authors: Philipp Westhoff, Mattia Moroder, Ulrich Schollwöck, Sebastian Paeckel,
• Abstract summary: We introduce a framework to compute not only steady states, but also low-lying excited states with unprecedented precision for large, driven quantum many-body systems.<n>This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit, or the environment-assisted, robust preparation of highly entangled states, demand a systematic analysis of quantum many-body phases out of equilibrium. 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. Here, we undertake a first step to overcome this limitation and introduce a tensor-network-based framework to compute systematically not only steady states, but also low-lying excited states with unprecedented precision for large, driven quantum many-body systems. Our 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. At the example of the interacting Bose-Hubbard model driven by dissipation-assisted hopping, we demonstrate the high efficiency and accuracy, enabling us to perform a reliable finite-size scaling analysis of the spectral gap and demonstrating the existence of anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.

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