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Out-of-time-ordered correlators in short-range and long-range hard-core boson models and Luttinger liquid model

Lin, Cheng-Ju and Motrunich, Olexei I. (2018) Out-of-time-ordered correlators in short-range and long-range hard-core boson models and Luttinger liquid model. Physical Review B, 98 (13). Art. No. 134305. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20180821-145330708

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Abstract

We study out-of-time-ordered correlators (OTOCs) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOCs in the Luttinger-liquid model. For density-density correlations, a related expectation value of the squared commutator starts at zero and decays back to zero after the passage of the wavefront in all three models, while the wavefront broadens as t^(1/3) in the short-range model and shows no broadening in the long-range model and the Luttinger-liquid model. For the boson creation operator, the corresponding commutator function shows saturation inside the light cone in all three models, with similar wavefront behavior as in the density-density commutator function, despite the presence of a nonlocal string in terms of Jordan-Wigner fermions. For the long-range model and the Luttinger-liquid model, the commutator function decays as a power law outside the light cone in the long-time regime when following different fixed-velocity rays. In all cases, the OTOCs approach their long-time values in a power-law fashion, with different exponents for different observables and short-range versus long-range cases. Our long-range model appears to capture exponents in the Luttinger-liquid model (which are found to be independent of the Luttinger parameter in the model). This conclusion also comes to bear on the OTOC calculations in conformal field theories, which we propose correspond to long-ranged models.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.98.134305DOIArticle
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.134305PublisherArticle
https://arxiv.org/abs/1807.08826arXivDiscussion Paper
ORCID:
AuthorORCID
Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2018 American Physical Society. Received 4 August 2018; revised manuscript received 22 September 2018; published 15 October 2018. The authors would like to thank Y.-Z. Chou, D. Huse, N. Hunter-Jones, V. Khemani, B. Swingle, and N. Yunger Halpern for useful discussions. 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, IQIM
Funders:
Funding AgencyGrant Number
NSFDMR-1619696
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20180821-145330708
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180821-145330708
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88992
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:21 Aug 2018 22:45
Last Modified:16 Oct 2018 19:59

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