Overcoming the Lamb Shift in System-Bath Models via KMS Detailed Balance: High-Accuracy Thermalization with Time-Bounded Interactions

Quantum Physics [Submitted on 17 Apr 2026] Overcoming the Lamb Shift in System-Bath Models via KMS Detailed Balance: High-Accuracy Thermalization with Time-Bounded Interactions Hongrui Chen, Zhiyan Ding, Ruizhe Zhang We investigate quantum thermal state preparation algorithms based on system-bath interactions and uncover a surprising phenomenon in the weak-coupling regime. We rigorously prove that, if the system-bath interaction is engineered so that the transition part of the approximate Lindbladian generator satisfies the KMS detailed balance condition, then the unique fixed point of the dynamics can be made arbitrarily close to the Gibbs state in the weak-coupling limit, regardless of the structure of the Lamb shift term. Importantly, this remains true even when the approximate Lindbladian differs substantially from the ideal Davies generator and the Lamb shift term does not commute with the thermal state. Our result shows that the role of the KMS detailed balance condition extends well beyond standard Lindbladian dynamics, serving as a general principle for a broader class of dissipative systems. Furthermore, by combining this with a general perturbation framework, we bound the mixing time of the dynamics and establish an end-to-end complexity of O(\varepsilon^{-1}) for Gibbs state preparation. These guarantees apply to any Hamiltonian for which the corresponding KMS-detailed-balance Lindbladian is known to mix rapidly. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15616 [quant-ph]   (or arXiv:2604.15616v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.15616 Focus to learn more Submission history From: Zhiyan Ding [view email] [v1] Fri, 17 Apr 2026 01:44:43 UTC (109 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)