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Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

Lin, Cheng-Ju and Motrunich, Olexei I. (2017) Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization. Physical Review B, 96 (21). Art. No. 214301. ISSN 2469-9950. doi:10.1103/PhysRevB.96.214301.

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We numerically construct translationally invariant quasiconserved operators with maximum range M, which best commute with a nonintegrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasiconserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasiconserved operator can be understood as a dressed total “spin-z” operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows an almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasiconserved operator.

Item Type:Article
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URLURL TypeDescription Paper
Lin, Cheng-Ju0000-0001-7898-0211
Motrunich, Olexei I.0000-0001-8031-0022
Alternate Title:Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization
Additional Information:© 2017 American Physical Society. Received 22 September 2017; published 12 December 2017. The authors would like to thank M. C. Bañuls, M. Serbyn, V. Khemani, and N. J. Robinson for valuable discussions at a poster session at Aspen Center for Physics where bulk of this work was presented in January 2017. We would also like to thank J. R. Garrison, R. V. Mishmash and M. P. A. Fisher for inspiring discussions of their work and C. White for discussions on the TEBD calculation. This work was supported by NSF through Grant No. DMR-1619696 and also by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center, with support of the Gordon and Betty Moore Foundation.
Group:Institute for Quantum Information and Matter
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Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:21
Record Number:CaltechAUTHORS:20171004-144618632
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82078
Deposited By: Joy Painter
Deposited On:05 Oct 2017 16:54
Last Modified:15 Nov 2021 19:48

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