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Cited by 99Quantum many-body systemsTheoretical and Computational PhysicsCold Atom Physics and Bose-Einstein Condensates

Quantum phase transition dynamics in the two-dimensional transverse-field Ising model

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Schmitt, Markus, Rams, Marek M., Dziarmaga, Jacek, Heyl, Markus, Zurek, Wojciech H.·2022·Science Advances
DOI 10.1126/sciadv.abl6850PMC PMC9481121
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Abstract

The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior near the quantum phase transitions (QPTs). It is now well understood for the one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by the fundamentally different character of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps toward theoretical exploration of the QKZM in two dimensions for interacting quantum matter. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods, including artificial neural networks and tensor networks. As a central result, we quantify universal QKZM behavior close to the QPT. We also note that, upon traversing further into the ferromagnetic regime, deviations from the QKZM prediction appear. We explain the observed behavior by proposing an extended QKZM taking into account spectral information as well as phase ordering. Our work provides a testing platform for higher-dimensional quantum simulators.

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  • For the problem of simulating non-adiabatic critical dynamics of the TFIM, the Kibble-Zurek mechanism has been studied with an NQS approach using tVMC.

    “For the problem at hand, which is the simulation of non-adiabatic critical dynamics of the TFIM, the Kibble-Zurek mechanism has been studied with an NQS approach that uses tVMC 48 .”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [48]

    The Results (Setting and methods) and Methods sections say the paper studies quantum Kibble–Zurek dynamics in the 2D Ising model using neural quantum states for time evolution. They describe convolutional neural networks and regularization techniques, but do not identify the NQS time-evolution method as tVMC; that specific part is not established by our copy. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • MPS, PEPS, and NQS are currently recognized as the leading approximation frameworks in this context.

    “MPS, PEPS, and NQS are currently recognized as the leading approximation frameworks in this context 48 .”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [48]

  • In both Ref.48 and Ref.57, NQS approaches are only used close to the critical point.

    “In both Ref.48 and Ref. 57, NQS approaches are only used close to the critical point.”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [48]

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References 80 · Cited by 99

Research works printed but not linked: 54

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Authors
Schmitt, M., Rams, M. M., Dziarmaga, J., Heyl, M., & Zurek, W. H.
Affiliations
  • University of Cologne (DE)
  • Jagiellonian University (PL)
  • University of Augsburg (DE)
  • Los Alamos National Laboratory (US)
Corresponding author
  • Schmitt, Markus
  • Rams, Marek M.
ORCID
Venue
Science Advances
Publisher
American Association for the Advancement of Science (AAAS)
Published
2022-09-16
Volume
8
Issue
37
Pages
eabl6850-eabl6850
ISSN
2375-2548 (ISSN-L)
DOI
10.1126/sciadv.abl6850
PMC
PMC9481121
OpenAlex
W3171317091
Cited by
99
References
80
Citations by year
2026: 20 · 2025: 29 · 2024: 20 · 2023: 18 · 2022: 7 · 2021: 5
FWCI
7.79
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Science Advances (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Kölner Universitäts PublikationsServer (Universität zu Köln) (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Homo Politicus (Academy of Humanities and Economics in Lodz) (submittedVersion, cc-by-nc-nd)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • OPUS (Augsburg University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • U.S. Department of Energy
  • European Commission (HORIZON2020, 2017/25/Z/ST2/03028, 853443)
  • Deutsche Forschungsgemeinschaft
  • Gottfried Wilhelm Leibniz Universität Hannover
  • Deutsche Akademie der Naturforscher Leopoldina - Nationale Akademie der Wissenschaften (LPDS 2018-07)
  • QuantERA
  • Gauss Centre for Supercomputing
  • Office of Science
  • Leibniz-Gemeinschaft
  • Basic Energy Sciences
  • Laboratory Directed Research and Development
  • Los Alamos National Laboratory
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
Keywords
quantum phase transitions, transverse-field Ising model, two-dimensional quantum systems, dynamic critical phenomena, phase ordering, spectral data, ferromagnetic phase, quantum simulators, artificial neural networks, tensor networks

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