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

• URL: http://arxiv.org/abs/2001.03421v4
• Date: Sat, 2 May 2020 07:39:50 GMT
• Title: Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
• Authors: Zongping Gong, Nobuyuki Yoshioka, Naoyuki Shibata, Ryusuke Hamazaki
• Abstract summary: We introduce a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. We generalize the result to isolated quantum many-body systems by employing the local Schrieffer-Wolff transformation.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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