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Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain

Lin, Cheng-Ju and Motrunich, Olexei I. (2017) Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain. Physical Review A, 95 (2). Art. No. 023621. ISSN 2469-9926. http://resolver.caltech.edu/CaltechAUTHORS:20161212-141040765

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Abstract

The eigenstate thermalization hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. Quench protocol is one of the settings to study such questions. A recent numerical study [Bañuls, Cirac, and Hastings, Phys. Rev. Lett. 106, 050405 (2007)] of a nonintegrable quantum Ising model with longitudinal field under such a quench setting found different behaviors for different initial quantum states. One particular case called the “weak-thermalization” regime showed apparently persistent oscillations of some observables. Here we provide an explanation of such oscillations. We note that the corresponding initial state has low energy density relative to the ground state of the model. We then use perturbation theory near the ground state and identify the oscillation frequency as essentially a quasiparticle gap. With this quasiparticle picture, we can then address the long-time behavior of the oscillations. Upon making additional approximations which intuitively should only make thermalization weaker, we argue that the oscillations nevertheless decay in the long-time limit. As part of our arguments, we also consider a quench from a BEC to a hard-core boson model in one dimension. We find that the expectation value of a single-boson creation operator oscillates but decays exponentially in time, while a pair-boson creation operator has oscillations with a t^(−3/2) decay in time. We also study dependence of the decay time on the density of bosons in the low-density regime and use this to estimate decay time for oscillations in the original spin model.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.95.023621DOIArticle
http://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.023621PublisherArticle
https://arxiv.org/abs/1610.04287arXivDiscussion Paper
ORCID:
AuthorORCID
Lin, Cheng-Ju0000-0001-7898-0211
Motrunich, Olexei I.0000-0001-8031-0022
Alternate Title:Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
Additional Information:© 2017 American Physical Society. (Received 2 November 2016; revised manuscript received 30 December 2016; published 22 February 2017) We gratefully acknowledge M. Fisher, J. Garrison, S. Gopalakrishnan, R. Mishmash, G. Refael, and C. White for many helpful discussions and also thank S. Gopalakrishnan for bringing Ref. [47] to our attention. We are particularly grateful to M. C. Bañuls, I. Cirac, and M. Hastings for sharing their infinite-MPS data used in Fig. 1 and for valuable comments on the paper and also for pointing us to Ref. [39]. We would also like to thank P. Calabrese and G. Delfino for bringing Refs. [26,27,41] to our attention. This work was supported by the NSF through Grants No. DMR-1206096 and No. DMR-1619696 and the Caltech 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, IQIM
Funders:
Funding AgencyGrant Number
NSFDMR-1206096
NSFDMR-1619696
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20161212-141040765
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161212-141040765
Official Citation:Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain Cheng-Ju Lin and Olexei I. Motrunich Phys. Rev. A 95, 023621
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72730
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Dec 2016 23:14
Last Modified:22 Aug 2019 18:47

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