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This research introduces a tensor-network framework capable of efficiently computing low-lying eigenstates and steady states for large, driven quantum many-body systems, addressing a significant bottleneck in simulating open quantum systems. By leveraging complex-time Krylov spaces, the method provides a robust toolbox for solving non-Hermitian eigenvalue problems in both Markovian and non-Markovian environments. The approach demonstrates high accuracy in modeling anomalous relaxation dynamics, offering a scalable solution for analyzing spectral properties in generic quantum systems.
A Tensor Network Framework for Lindbladian Spectra and Steady States
arXiv:2509.07709v2 Announce Type: replace 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 dissipative state preparation 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 systematically compute not only steady states, but also low-lying excited states 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. From a reliable finite-size scaling analysis of the spectral gap, we find strong evidence for nonlinear hydrodynamic behavior consistent with Kardar-Parisi-Zhang-type superdiffusive relaxation and establish the existence of exponentially accelerated, anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.
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 dissipative state preparation 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 systematically compute not only steady states, but also low-lying excited states 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. From a reliable finite-size scaling analysis of the spectral gap, we find strong evidence for nonlinear hydrodynamic behavior consistent with Kardar-Parisi-Zhang-type superdiffusive relaxation and establish the existence of exponentially accelerated, anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Computational Physics (physics.comp-ph)
arXiv:2509.07709 [quant-ph]
(or arXiv:2509.07709v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2509.07709 Focus to learn more arXiv-issued DOI via DataCite
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