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

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.

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