English

Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations

Quantum Physics 2020-05-29 v4 Quantum Gases Statistical Mechanics Strongly Correlated Electrons Mathematical Physics math.MP

Abstract

In arXiv:2001.03419 we introduce a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. Here, we provide the full details on the derivation of the bound. In addition, we generalize the result to isolated quantum many-body systems by employing the local Schrieffer-Wolff transformation, obtaining an error bound that grows polynomially in time. We also generalize the result to Markovian open quantum systems and quantitatively explain the quantum Zeno effect.

Keywords

Cite

@article{arxiv.2001.03421,
  title  = {Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations},
  author = {Zongping Gong and Nobuyuki Yoshioka and Naoyuki Shibata and Ryusuke Hamazaki},
  journal= {arXiv preprint arXiv:2001.03421},
  year   = {2020}
}

Comments

19 pages, 9 figures. Accompanying letter arXiv:2001.03419. Here, we prove the exact (rather than asymptotic) bound and rigorously derive the many-body bound without numerical demonstration. Generalization to open systems is also discussed

R2 v1 2026-06-23T13:07:54.686Z