Space and time renormalization in phase transition dynamics
Open accessAbstract
When a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time $\ensuremath{\tau}$ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$ set at the time $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{t}=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\tau}}$ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigating an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.
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Quantum phase transitions are generically accompanied by critical slowing down close to the critical point.
“Generically, quantum phase transitions are accompanied by a critical slowing down close to the critical point [171,172].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [172]
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- Authors
- Francuz, A., Dziarmaga, J., Gardas, B., & Zurek, W. H.
- Affiliations
- Jagiellonian University (PL)
- Los Alamos National Laboratory (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2016-02-18
- Volume
- 93
- Issue
- 7
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2147335496
- Cited by
- 83
- References
- 95
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 8 · 2023: 3 · 2022: 9 · 2021: 6 · 2020: 14 · 2019: 10 · 2018: 6 · 2017: 11 · 2016: 8
- FWCI
- 5.52
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- 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)
- arXiv (Cornell University)
- Funders
- Narodowe Centrum Nauki (DEC-2013/09/B/ST3/01603)
- U.S. Department of Energy
- 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 › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- Kibble-Zurek mechanism, quantum critical point, nonadiabatic dynamics, critical slowing down, spatiotemporal scaling, renormalization, exact solutions, thermodynamic limit, correlation length
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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