A Tensor Network Framework for Lindbladian Spectra and Steady States
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916942871265280 |
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| author | Westhoff, Philipp Moroder, Mattia Schollwöck, Ulrich Paeckel, Sebastian |
| author_facet | Westhoff, Philipp Moroder, Mattia Schollwöck, Ulrich Paeckel, Sebastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Tensor Network Framework for Lindbladian Spectra and Steady States Westhoff, Philipp Moroder, Mattia Schollwöck, Ulrich Paeckel, Sebastian Quantum Physics Quantum Gases Computational Physics 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. |
| title | A Tensor Network Framework for Lindbladian Spectra and Steady States |
| topic | Quantum Physics Quantum Gases Computational Physics |
| url | https://arxiv.org/abs/2509.07709 |