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Cited by 82Quantum many-body systemsQuantum Information and CryptographyTheoretical and Computational Physics

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

Open access
Canovi, Elena, Ercolessi, Elisa, Naldesi, Piero, Taddia, Luca, Vodola, Davide·2014·Physical Review B
DOI 10.1103/physrevb.89.104303
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Abstract

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the transverse-field Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale $\ensuremath{\tau}$. The time evolution of the entanglement entropy displays different regimes depending on the value of $\ensuremath{\tau}$, showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of the entanglement entropy and Schmidt gap.

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Crossref · 10.1103/physrevb.89.104303

Cites

49 of 49 references verified0 citation errors · 0 not checkable

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  • Quenched quantum dynamics deviating from the ground state also show area-law scaling.

    “As discussed in Section V, and in agreement with previous observations 31 , we show that quenched quantum dynamics deviating from the ground state also show area-law scaling.”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [31]

    In §F.1 (Entanglement entropy; page unavailable), the paper reports that entropy curves for different system sizes are practically coincident at small quench times, consistent with size-independent scaling in that regime. Its discussion of fast sweeps (§D; page unavailable) describes dynamics that depart from the instantaneous ground state. It does not establish area-law scaling for quenched dynamics generally, as the claim implies. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

  • In a finite system, there is a crossover between the adiabatic and excited regimes, where in the adiabatic regime the entanglement entropy at the critical point is S ∝ log(N).

    “Focusing on a finite system 31 , there is a crossover between those two regimes, where, in the adiabatic regime, the entanglement entropy at the critical point is S ∝ log(N ) 118 .”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [31]

    Section III C says that in a finite system, entanglement entropy follows its ground-state value during a sufficiently slow, adiabatic sweep. The Entanglement entropy subsection gives logarithmic scaling with correlation length in an infinite system and with sweep time after a quench, but does not state the cited claim’s S ∝ log(N) scaling at the critical point in a finite system. The crossover portion of the citing sentence carries a different citation. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

  • In a homogeneous 1D transverse-field Ising model, at the end of the anneal the entanglement entropy grows logarithmically as a function of annealing time t_a, S(t = t_a) ∝ log(t_a).

    “Entanglement dynamics in such a case has been studied in a homogeneous 1D TFIM in Refs.31,112, showing that at the end of the anneal it grows logarithmically as a function of annealing time t a , S(t = t a ) ∝ log(t a ).”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [31]

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Cites

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Research works printed but not linked: 2

  1. A. Zamora, J. Rodriguez-Laguna, M. Lewenstein, and L. Tagliacozzo, arXiv:1401.7916. · arXiv
  2. G. Torlai, L. Tagliacozzo, and G. De Chiara, arXiv:1311.5509. · arXiv

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Authors
Canovi, E., Ercolessi, E., Naldesi, P., Taddia, L., & Vodola, D.
Affiliations
  • University of Stuttgart (DE)
  • Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (IT)
  • Centre National de la Recherche Scientifique (FR)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2014-03-31
Volume
89
Issue
10
Pages
104303
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.89.104303
OpenAlex
W1986108732
Cited by
82
References
49
Citations by year
2026: 4 · 2025: 6 · 2024: 6 · 2023: 8 · 2022: 7 · 2021: 6 · 2020: 7 · 2019: 3 · 2018: 6 · 2017: 13 · 2016: 8 · 2015: 4 · 2014: 4
FWCI
4.81
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • HAL (submittedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) (submittedVersion)
  • arXiv (Cornell University)
Funders
Università di Bologna
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
Keywords
entanglement entropy, entanglement spectrum, quantum phase transitions, transverse-field Ising model, time-dependent magnetic field, finite systems, Kibble-Zurek scaling, entanglement oscillations

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