New Tensor Network Framework Enables Analysis of Quantum Systems in Non-Equilibrium States
Researchers have introduced a tensor-network-based computational framework capable of systematically computing steady states and low-lying excited states of Lindbladian operators governing large, driven open quantum many-body systems. The method builds on complex-time Krylov space techniques to address the non-Hermitian eigenvalue problem that arises when quantum systems interact with Markovian or non-Markovian environments. This advance could enable systematic study of non-equilibrium quantum phases and dissipative state preparation that were previously inaccessible to conventional simulation approaches.
A team of researchers has developed a tensor-network framework designed to compute the low-lying eigenspectrum of Lindbladians — the operators describing the evolution of open quantum systems coupled to external environments. Unlike equilibrium methods, this approach targets the non-Hermitian eigenvalue problem inherent to open systems and extends to both Markovian and non-Markovian environments. The framework leverages recent advances in complex-time Krylov space methods, assembling them into a toolbox tailored for large, driven quantum many-body systems. As a demonstration, the authors applied the method to the interacting Bose-Hubbard model under dissipation-assisted hopping, performing finite-size scaling analysis of the spectral gap. The results provide strong evidence for nonlinear hydrodynamic behavior consistent with Kardar-Parisi-Zhang (KPZ)-type superdiffusive relaxation, and additionally establish the existence of exponentially accelerated anomalous relaxation. The work represents a first systematic step toward spectral analysis of generic open quantum many-body systems, with potential implications for realizing unconventional non-equilibrium phases beyond the Mermin-Wagner limit and for dissipative quantum state preparation.
What's missing
The paper is a preprint on arXiv and has not yet undergone formal peer review, so its results have not been independently validated. The study's own scope is limited to one model system (the Bose-Hubbard model) as a proof of concept; the computational scaling and practical limits of the framework for more complex or higher-dimensional systems are not fully characterized. The physical interpretation of the KPZ-type behavior and anomalous relaxation remains to be confirmed by independent numerical or experimental studies.
What different sources said
- arXiv physicsCenter
A Tensor Network Framework for Lindbladian Spectra and Steady States
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