Cluster Ising quantum batteries can mimic super-extensive charging power

Anna Pavone; Dario Ferraro; Federico Luigi Cavagnaro; Matteo Carrega; Niccol\`o Traverso Ziani; Riccardo Grazi

REVIEW 3 major objections 5 minor 46 references

Cluster Ising quantum batteries can mimic super-extensive charging power

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that an extended cluster-Ising model, though exactly solvable via Jordan-Wigner fermionization, exhibits super-extensive charging power — maximum average power scaling as N^0.83 and N^0.89 — over finite chains up to about a

desk verdict Credible finite-size mimicry of super-extensive charging, but the headline exponents need a larger-N check and reported parameters before they stand. read the letter →

arxiv 2602.15467 v2 pith:KNFLRBHG submitted 2026-02-17 quant-ph cond-mat.mes-hall

Anna Pavone , Federico Luigi Cavagnaro , Matteo Carrega , Riccardo Grazi , Dario Ferraro , Niccolò Traverso Ziani This is my paper · ORCID

classification quant-phcond-mat.mes-hall

keywords quantumbatteriessuper-extensivechargingpowercluster-IsingmodelintegrablespinchainsJordan-Wignertransformationfinite-sizeeffectsquenchstoredenergyscaling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum batteries are devices that store and release energy, and their appeal depends partly on whether charging power can grow faster than the number of constituent spins, a property called super-extensive scaling. This paper studies two variants of the cluster-Ising spin chain, both exactly solvable by mapping to free fermions, and claims that, contrary to the widespread expectation for such integrable chains, they do show super-extensive charging power in wide finite-size windows. For a fixed cluster interaction range, the fitted exponents are about 0.83 and 0.89 for the two models, up to about 10^3 spins. The authors identify the mechanism: the stored energy itself grows super-extensively, not the optimal charging time, so the effect is a finite-size phenomenon that cannot survive the thermodynamic limit. A sympathetic reader should care because this blurs the boundary between genuine collective quantum advantage and finite-size artifacts in quantum battery proposals.

What carries the argument

The central object is the multi-spin cluster interaction O^z_{j,n} = ∏_{k=1}^n σ^z_{j+k}, whose range n is the tunable control parameter. Jordan-Wigner fermionization followed by a Fourier transform reduces both models to non-interacting Bogoliubov-de Gennes form H_q = A_q τ^z + C_q τ^x, so the double-quench dynamics becomes a sum of independent two-level rotations. The exact energy formula (Eq. 16) is the tool that permits power-law fits of P^M(N); the mechanism carrying the claim is that the super-extensive scaling enters through the stored energy, not through a favorable scaling of the optimal charging time.

What would settle it

Extend the numerical data for fixed n=15 to larger N (e.g., 1000–10000) and plot log P^M versus log N: if the local slope decays toward zero or shows visible curvature as N grows, the super-extensive exponents are finite-size transients rather than a stable scaling property. Reproducing Fig. 2 also requires the battery and charging angles φ^(B) and φ^(C), which the paper never reports; publishing those values together with one extended-range curve would settle the claim.

Watch

Extended reading notes

Core claim

For two generalized cluster-Ising Hamiltonians H1 and H2, the battery is prepared in the ground (or thermal) state of the Hamiltonian with parameters φ^(B), then charged by a sudden quench to parameters φ^(C) for a time τ. The stored energy per spin has an exact closed form as a sum over momenta, and the maximum average charging power is obtained by numerically maximizing over τ. The paper's central numerical finding is that, at fixed cluster range n=15, P^M(N) follows a power law with exponents α≈0.83 for H1 and α≈0.89 for H2; when n is scaled with N as N^{1/2} or N^{2/3}, the exponents drop to roughly 0.48–0.50 and 0.30–0.36, respectively. The authors argue that this anomalous scaling orig

Load-bearing premise

The load-bearing premise is that the power-law fits over the chosen finite ranges of N (e.g., 169–324 for H1) capture the model's genuine scaling behavior; since the stored energy per spin is bounded for fixed n, the growth must eventually saturate, and the reported quench angles are never listed, so the fits cannot be independently reproduced.

Editorial extensions

If this is right

If correct, the result gives a concrete counterexample to the common expectation that Jordan-Wigner integrable spin chains cannot achieve super-extensive charging power under quantum-quench protocols.
The super-extensive power is a finite-size effect: for fixed n it cannot persist as N→∞, so claims of quantum advantage from such chains must specify the crossover scale.
Because the stored energy drives the scaling, faster charging here means storing more energy per spin, not charging in proportionally shorter time.
The effect survives at finite temperature (β=1) with qualitatively the same trends, so thermal noise alone does not erase the enhancement.
Scaling the cluster range n with N degrades the exponent (≈0.48–0.50 for n=N^{1/2}, ≈0.30–0.36 for n=N^{2/3}), suggesting the enhancement is strongest at fixed finite interaction range.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An extension the paper leaves implicit: the suggested P^M ∝ N/n tendency, if proven analytically from the q-sum energy formula, would unify the fixed-n and scaling-n cases into a single mechanism; evaluating that sum at large N is a direct test.
The result is a cautionary tale for neighboring battery models: any super-extensive fit in an integrable or near-integrable system should be checked against the Hamiltonian-norm bound to distinguish genuine collective advantage from finite-size transients.
The mechanism depends mainly on the cluster string's range, so similar finite-size super-extensive energy growth may appear in other free-fermion chains with long-range string interactions, not only in these two cluster-Ising variants.
A testable experimental fingerprint: in a chain of roughly 10^2–10^3 spins with engineered multi-spin interactions, the maximum charging power should grow faster than N while the optimal charging time stays approximately scale-free; measuring both would confirm or rule out the mechanism.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here is my read on Pavone et al. The paper does something real: for two cluster-Ising models it derives an exact expression for stored energy after a double quench, Eq. (16), and shows numerically that in a finite range of N the maximum charging power grows faster than linearly. The mechanism is clear: the stored energy itself grows super-extensively, not the optimal charging time. That is a direct challenge to the common assumption that JW-integrable chains cannot do this. The authors are honest that it is a finite-size effect that cannot persist in the thermodynamic limit, and they include an appendix with cases where the scaling is only extensive or sub-extensive. Good.

The soft spots. The headline exponents (α≈0.83 for H1, 0.89 for H2) are fitted over narrow windows: N=169–324 for H1, a range factor of 1.9, and N=36–196 for H2, with no error bars and no scaling collapse. Eq. (16) is a single sum over N modes, so extending to N=10^4 or 10^5 is trivial. Not doing it is the main gap. Since the energy per spin is bounded by the Hamiltonian norm, the growth has to saturate; without a larger-N scan or an asymptotic estimate, the fitted exponents could be artifacts of a short monotone interval. The abstract's 'up to a thousand spins' is also generous: the 0.8 exponents are demonstrated only up to N=324; when n scales as N^{2/3}, the exponent drops to about 0.3 even at N=5000. The paper frames this correctly as mimicry, but the high-exponent regime is even more finite than the abstract suggests.

A separate problem: the quench angles φ^(B/C) are never reported. The figures are therefore not reproducible. That is fixable but real.

Overall, the physics is plausible, the exact formula is a solid foundation, and the paper is honest. It deserves serious review. The referee should ask for reported parameters, error bars and a scaling collapse, and a large-N scan with Eq. (16) to show the saturation crossover. I would bring it to a reading group and would cite it in work on quantum battery bounds.

Referee Report

3 major / 5 minor

Summary. The paper studies two cluster-Ising spin-chain Hamiltonians, solved by Jordan-Wigner transformation and Fourier decomposition into a Bogoliubov-de Gennes form. The proposed quantum battery is charged by a double quench in the angular parameter φ, and the authors derive a closed-form expression, Eq. (16), for the energy stored per spin. They then numerically evaluate the maximum average charging power P^M over the charging time τ. The central claim is that, despite the models being Wigner-Jordan integrable, P^M displays an apparent super-extensive scaling P^M ∝ N^α in finite systems, with fitted exponents α ≈ 0.83 (H1) and α ≈ 0.89 (H2) for fixed n = 15, and smaller exponents for n = N^{1/2} and n = N^{2/3}. The authors emphasize that this enhancement comes from the stored energy itself, not from a favorable scaling of τ_max, and that it cannot survive in the thermodynamic limit. A brief appendix shows regimes where the enhancement is absent.

Significance. If the reported scaling is correct, the paper would refine the general belief that Wigner-Jordan integrable spin-chain batteries cannot exhibit super-extensive charging power, showing that finite-size effects can mimic such enhancement in an exactly solvable setting. The exact closed form of Eq. (16) is a genuine strength, since it allows precise numerical evaluation and, in principle, rigorous asymptotic analysis. The paper also frames the result honestly as a finite-size phenomenon rather than a thermodynamic-limit effect. However, the current numerical evidence for the specific exponents is not strong enough to support the central claim, and the unreported quench parameters prevent independent verification.

major comments (3)

[§III, Eq. (16)] I cannot reproduce the prefactor in Eq. (16) from the standard double-quench two-level calculation. For a single mode with H_B = A_B τ_z + C_B τ_x and H_C = A_C τ_z + C_C τ_x, the excess energy measured with respect to H_B after evolving for time τ under H_C is ΔE_q = [(C_B A_C - A_B C_C)^2/(ε_q ω_q^2)] [1 - cos(2 ω_q τ)], with ε_q = sqrt(A_B^2 + C_B^2) and ω_q = sqrt(A_C^2 + C_C^2). Equation (16) contains an additional factor 1/2 in the denominator. This would change all reported energies and powers by a factor of 2, even if the scaling exponents are unaffected. Please provide the derivation or explicitly state the Nambu normalization used in Eq. (8).
[§IV, Figs. 2–4] The central scaling claim rests on power-law fits over narrow system-size windows: H1 fixed-n uses N = 169–324 (a factor of ~1.9), H2 uses N = 36–196, n = N^{1/2} uses N ≈ 150–350, and n = N^{2/3} uses N ≈ 3000–5000. No error bars, residuals, or scaling collapse are shown. Since Eq. (16) is an exact single sum and the per-spin stored energy is bounded by O(1), the observed growth must saturate at some N. A monotonically increasing but eventually saturating function can easily mimic a power law over such short intervals. The authors should evaluate Eq. (16) to much larger N (or provide an Euler–Maclaurin asymptotic expansion around the modes where ε(q) is small) and demonstrate that the fitted exponents stabilize. They should also locate the crossover to saturation and show that the claimed exponents are not an artifact of the chosen windows.
[§IV, all figures] The values of the quench angles φ_1/2^(B) and φ_1/2^(C) used in the numerical evaluation are never reported. The statement that the physics is 'qualitatively independent' of these angles does not allow reproduction, especially because the Appendix shows that the super-extensive behavior is parameter-sensitive (e.g., n = N/2 and n = N^{1/3} do not show it). Please list all parameter values for every figure and test the fitted exponents over a range of angles, with error estimates.

minor comments (5)

[Abstract / §IV] The abstract says 'reaching up to a thousand spins', but for fixed n = 15 the displayed H1 data stop at N = 324 and H2 at N = 196; only the n = N^{2/3} case reaches N ≈ 5000. This should be clarified to avoid overstating the fixed-n results.
[§V, Conclusions] The final paragraph suggests P^M ∝ N/n. For fixed n this would predict a linear scaling α ≈ 1, inconsistent with the fitted α ≈ 0.83 for H1. Please clarify whether the N/n scaling is only an asymptotic statement for n growing with N, and specify the regime of validity.
[§IV, Fig. 5] In the Appendix, panel (a) is described as showing a regime where the power 'approaches the extensive regime.' For a per-spin quantity, extensivity corresponds to α = 0, i.e., a flat curve, which is consistent with the figure. The wording may confuse readers who associate 'extensive' with linear total power; define the convention used.
[§III, Eq. (20)] No numerical details are given for the maximization over τ defining P^M. Please state the grid resolution or optimization procedure used to identify τ_max, since the fitted exponents could be sensitive to under-sampling of the oscillatory function in Eq. (16).
[§II, Eqs. (4)–(6)] The Jordan-Wigner transformation is written with some missing phase and index details. In particular, Eq. (5) and (6) should specify the convention for σ^±_j more carefully; a reader reconstructing the BdG form will need these conventions explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: exact formula evaluated numerically; scaling exponents are outputs, not inputs.

full rationale

The derivation chain is: define the cluster-Ising Hamiltonians H1 and H2, map them to free fermions via Jordan-Wigner and Fourier transforms, derive the exact closed-form stored energy per spin E_{1/2}(τ) in Eq. (16), obtain the average charging power as P = E/τ, maximize numerically over τ, and finally fit the resulting P^M(N) to a power law. None of these steps uses the claimed super-extensive exponent as an input: the quench angles and the cluster range n are set before evaluating the formula, and the fitted exponents (α≈0.83 and α≈0.89) are summaries of the numerical data, not parameters inserted into Eq. (16). The paper explicitly acknowledges that the effect is a finite-size enhancement that cannot persist in the thermodynamic limit, so the boundedness of the stored energy does not make the scaling claim circular. Self-citations [17,38,39] are contextual and not load-bearing; the no-go attribution is to the external reference [13]. The un-reported quench-angle values and narrow N windows are reproducibility and statistical-robustness concerns, not circular reductions. No equation or fitted parameter is equivalent by construction to the claimed result. Therefore no significant circularity is found.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim does not introduce new physical entities. It relies on standard many-body techniques (Jordan-Wigner, Fourier/Bogoliubov diagonalization) and on a set of domain assumptions about the parity sector, the initial state, and the numerical maximization. The free parameters are the quench angles (unreported values) and the fitted power-law exponents/prefactors that constitute the evidence for the scaling claim.

free parameters (5)

φ^{(B)}_{1/2}, φ^{(C)}_{1/2} (quench angles) = not reported
The entire numerical study depends on these Hamiltonian parameter values, but they are never specified in the text or captions, so every figure is underdetermined.
α for fixed n=15 = α1≈0.8327, α2≈0.8933
Exponents from power-law fits of P^M(N) in Fig. 2; these fitted values are the evidence for super-extensive scaling.
α for n=N^{1/2} = α1≈0.4766, α2≈0.4989
Exponents from fits in Fig. 3(a,b).
α for n=N^{2/3} = α1≈0.3015, α2≈0.3561
Exponents from fits in Fig. 3(c,d).
prefactors a1,a2 = varies per case (e.g., a1≈0.00019, a2≈0.001 for fixed n)
Amplitudes in the fits P^M = a N^α; listed in captions but not used in a predictive way.

assumptions (5)

standard math Jordan-Wigner transformation maps the cluster-Ising Hamiltonians H1 and H2 to free-fermion Hamiltonians diagonalizable by Fourier transform
Invoked in Section II, Eqs. (4)–(8); relies on the specific form of the cluster interactions and periodic boundary conditions.
domain assumption The dynamics is restricted to the odd fermion parity sector, which 'does not qualitatively alter the results'
Section II, final paragraph; the initial state is not specified to be in this sector, so this restriction is an assumption about the physics.
standard math The initial state is the ground state (T=0) or a Gibbs state at inverse temperature β of the pre-quench Hamiltonian, and the evolution is unitary
Section III, Eq. (15) and text; standard quench protocol assumption.
domain assumption The maximum over τ of the averaged power is attained at a finite τ and is found reliably by numerical maximization
Section III, Eq. (20); no proof of uniqueness or numerical precision is given.
domain assumption The stored energy per spin does not scale with N in the thermodynamic limit
Statement after Eq. (18); used to argue that the observed super-extensive scaling is finite-size, but no explicit derivation for all parameter regimes is provided.

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Cite this review

Pith. "Pith review of Cluster Ising quantum batteries can mimic super-extensive charging power." pith.science (2026). https://pith.science/paper/KNFLRBHG

@misc{pith2026260215467,
  author       = {Pith},
  title        = {Pith review of: Cluster Ising quantum batteries can mimic super-extensive charging power},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KNFLRBHG}},
  note         = {Machine review of arXiv:2602.15467}
}

read the original abstract

Quantum batteries, miniaturized devices able to store and release energy on demand, are promising both because their intrinsic energy and time scales can match those of other quantum technologies and due to the intriguing possibility of achieving super-extensive charging power. While this enhanced scaling is known to appear in several settings, it is generally believed to be forbidden in Jordan-Wigner integrable spin chains charged via quantum-quench protocols. Here, we show that an extended cluster-Ising model, despite belonging to the above category, exhibits super-extensive charging power over wide ranges of system sizes, reaching up to a thousand spins, in proper parameter regimes. This remarkable anomalous scaling is due to a corresponding super-extensive growth of the stored energy, implying that it is limited to a large but finite size of the system and cannot persist in the thermodynamic limit. This phenomenon appears robust against finite-temperature effects.

Figures

Figures reproduced from arXiv: 2602.15467 by the authors.

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Works this paper leans on

46 extracted references · 2 linked inside Pith

[1]

Ezratty,Understanding Quantum Technologies (2024), arXiv:2111.15352 [quant-ph]

O. Ezratty,Understanding Quantum Technologies (2024), arXiv:2111.15352 [quant-ph]

arXiv 2024
[2]

Aguado, R

R. Aguado, R. Citro, M. Lewenstein, and M. Stern,New Trends and Platforms for Quantum Technologies, Lecture 6 Notes in Physics Vol. 1025 (Springer Nature Switzerland, Cham, 2024)

2024
[3]

J. Q. Quach, G. Cerullo, and T. Virgili, Quantum batter- ies: The future of energy storage?,Joule7, 2195 (2023)

2023
[4]

Campaioli, S

F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries,Rev. Mod. Phys.96, 031001 (2024)

2024
[5]

Camposeo, T

A. Camposeo, T. Virgili, F. Lombardi, G. Cerullo, D. Pisignano, and M. Polini, Quantum batteries: A materi- als science perspective,Adv. Mater.37, 2415073 (2025)

2025
[6]

Ferraro, F

D. Ferraro, F. Cavaliere, M. G. Genoni, G. Benenti, and M. Sassetti, Opportunities and challenges of quantum batteries,Nat. Rev. Phys.(2026), doi:10.1038/s42254- 025-00906-5

doi:10.1038/s42254- 2026
[7]

G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Charger-mediated energy transfer in exactly solvable models for quantum batteries, Phys. Rev. B98, 205423 (2018)

2018
[8]

F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: Powerful charging of quantum batteries, New J. Phys.17, 075015 (2015)

2015

Show all 46 references

[9]

Campaioli, F

F. Campaioli, F. A. Pollock, F. C. Binder, L. C´ eleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries,Phys. Rev. Lett. 118, 150601 (2017)

2017
[10]

L. Gao, C. Cheng, W.-B. He, R. Mondaini, X.-W. Guan, and H.-Q. Lin, Scaling of energy and power in a large quantum battery-charger model,Phys. Rev. Res. 4, 043150 (2022)

2022
[11]

C.-K. Hu, C. Liu, J. Zhao, L. Zhong, Y. Zhou, M. Liu, H. Yuan, Y. Lin, Y. Xu, G. Hu, G. Xie, Z. Liu, R. Zhou, Y. Ri, W. Zhang, R. Deng, A. Saguia, X. Linpeng, M. S. Sarandy, S. Liu, A. C. Santos, D. Tan, and D. Yu, Quan- tum charging advantage in superconducting solid-state ba...

2026
[12]

G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Quantum versus classical many-body batter- ies,Phys. Rev. B99, 205437 (2019)

2019
[13]

Juli` a-Farr´ e, T

S. Juli` a-Farr´ e, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Bounds on the capacity and power of quantum batteries,Phys. Rev. Res.2, 023113 (2020)

2020
[14]

Francica, Quantum correlations and ergotropy,Phys

G. Francica, Quantum correlations and ergotropy,Phys. Rev. E105, L052101 (2022)

2022
[15]

Gyhm and U

J.-Y. Gyhm and U. R. Fischer, Beneficial and detrimental entanglement for quantum battery charging,A VS Quan- tum Sci.6, 012001 (2024)

2024
[16]

Hokkyo and M

A. Hokkyo and M. Ueda, Universal upper bound on er- gotropy and no-go theorem by the eigenstate thermaliza- tion hypothesis,Phys. Rev. Lett.134, 010406 (2025)

2025
[17]

Cavaliere, D

F. Cavaliere, D. Ferraro, M. Carrega, G. Benenti, and M. Sassetti, Quantum advantage bounds for a multipartite Gaussian battery, arXiv:2510.24162 [quant-ph] (2025)

2025
[18]

Ferraro, M

D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, High-power collective charging of a solid- state quantum battery,Phys. Rev. Lett.120, 117702 (2018)

2018
[19]

Gemme, G

G. Gemme, G. M. Andolina, F. M. D. Pellegrino, M. Sassetti, and D. Ferraro, Off-resonant Dicke quantum battery: Charging by virtual photons,Batteries9, 202 (2023)

2023
[20]

J. Q. Quach, K. E. McGhee, L. Ganzer, D. M. Rouse, B. W. Lovett, E. M. Gauger, J. Keeling, G. Cerullo, D. Lidzey, and T. Virgili, Superabsorption in an organic microcavity: Toward a quantum battery,Sci. Adv.8, eabk3160 (2022)

2022
[21]

Carrasco, J

J. Carrasco, J. R. Maze, C. Hermann-Avigliano, and F. Barra, Collective enhancement in dissipative quantum batteries,Phys. Rev. E105, 064119 (2022)

2022
[22]

Wang, S.-Q

L. Wang, S.-Q. Liu, F.-L. Wu, H. Fan, and S.-Y. Liu, Deep strong charging in a multiphoton anisotropic Dicke quantum battery,Phys. Rev. A110, 042419 (2024)

2024
[23]

Yang, F.-M

D.-L. Yang, F.-M. Yang, and F.-Q. Dou, Three-level Dicke quantum battery,Phys. Rev. B109, 235432 (2024)

2024
[24]

Canzio, V

A. Canzio, V. Cavina, M. Polini, and V. Giovannetti, Single-atom dissipation and dephasing in Dicke and Tavis–Cummings quantum batteries,Phys. Rev. A111, 022222 (2025)

2025
[25]

D. J. Tibben, E. Della Gaspera, J. van Embden, P. Rei- neck, J. Q. Quach, F. Campaioli, and D. E. G´ omez, Ex- tending the self-discharge time of Dicke quantum bat- teries using molecular triplets,PRX Energy4, 023012 (2025)

2025
[26]

Kurman, K

Y. Kurman, K. Hymas, A. Fedorov, W. J. Munro, and J. Quach, Powering quantum computation with quantum batteries,Phys. Rev. X16, 011016 (2026)

2026
[27]

Hymaset al., Experimental demonstration of a scalable room-temperature quantum battery, arXiv:2501.16541 [quant-ph] (2025)

K. Hymaset al., Experimental demonstration of a scalable room-temperature quantum battery, arXiv:2501.16541 [quant-ph] (2025)

2025 arXiv
[28]

Rossini, G

D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Quantum advantage in the charging process of Sachdev–Ye–Kitaev batteries,Phys. Rev. Lett.125, 236402 (2020)

2020
[29]

D. Rosa, D. Rossini, G. M. Andolina, M. Polini, and M. Carrega, Ultra-stable charging of fast-scrambling SYK quantum batteries,J. High Energy Phys.2020, 067 (2020)

2020
[30]

G. M. Andolina, V. Stanzione, V. Giovannetti, and M. Polini, Genuine quantum advantage in anharmonic bosonic quantum batteries,Phys. Rev. Lett.134, 240403 (2025)

2025
[31]

T. P. Le, J. Levinsen, K. Modi, M. M. Parish, and F. A. Pollock, Spin-chain model of a many-body quantum bat- tery,Phys. Rev. A97, 022106 (2018)

2018
[32]

Rossini, G

D. Rossini, G. M. Andolina, and M. Polini, Many-body localized quantum batteries,Phys. Rev. B100, 115142 (2019)

2019
[33]

Ghosh, T

S. Ghosh, T. Chanda, and A. Sen(De), Enhancement in the performance of a quantum battery by ordered and disordered interactions,Phys. Rev. A101, 032115 (2020)

2020
[34]

M. B. Arjmandi, H. Mohammadi, and A. C. Santos, En- hancing self-discharging process with disordered quan- tum batteries,Phys. Rev. E105, 054115 (2022)

2022
[35]

Catalano, S

A. Catalano, S. Giampaolo, O. Morsch, V. Giovannetti, and F. Franchini, Frustrating quantum batteries,PRX Quantum5, 030319 (2024)

2024
[36]

J.-Y. Gyhm, D. ˇSafr´ anek, and D. Rosa, Quantum charg- ing advantage cannot be extensive without global opera- tions,Phys. Rev. Lett.128, 140501 (2022)

2022
[37]

Aliet al., Kitaev quantum batteries: Superexten- sive scaling of ergotropy in a 1D spin-1/2 XY-γchain, arXiv:2411.14074 [quant-ph] (2024)

A. Aliet al., Kitaev quantum batteries: Superexten- sive scaling of ergotropy in a 1D spin-1/2 XY-γchain, arXiv:2411.14074 [quant-ph] (2024)

2024 arXiv
[38]

Grazi, D

R. Grazi, D. Sacco Shaikh, M. Sassetti, N. Traverso Ziani, and D. Ferraro, Controlling energy storage crossing quan- tum phase transitions in an integrable spin quantum bat- tery,Phys. Rev. Lett.133, 197001 (2024). 7

2024
[39]

Grazi, F

R. Grazi, F. Cavaliere, M. Sassetti, D. Ferraro, and N. Traverso Ziani, Charging free fermion quantum batteries, Chaos Solitons Fractals196, 116383 (2025)

2025
[40]

Franchiniet al.,An Introduction to Integrable Tech- niques for One-Dimensional Quantum Systems, Lecture Notes in Physics Vol

F. Franchiniet al.,An Introduction to Integrable Tech- niques for One-Dimensional Quantum Systems, Lecture Notes in Physics Vol. 940 (Springer, 2017)

2017
[41]

Smacchia, L

P. Smacchia, L. Amico, P. Facchi, R. Fazio, G. Florio, S. Pascazio, and V. Vedral, Statistical mechanics of the cluster Ising model,Phys. Rev. A84, 022304 (2011)

2011
[42]

Ding, Phase transitions of a cluster Ising model,Phys

C. Ding, Phase transitions of a cluster Ising model,Phys. Rev. E100, 042131 (2019)

2019
[43]

Kheiri, R

S. Kheiri, R. Jafari, S. Mahdavifar, S. E. N. Oskoee, and A. Akbari, Dynamical phase diagram of the quantum Ising model with cluster interaction under noiseless and noisy driven field,Sci. Rep.15, 44339 (2025)

2025
[44]

Jordan and E

P. Jordan and E. Wigner, ¨Uber das Paulische ¨Aquivalenzverbot,Z. Phys.47, 631 (1928)

1928
[45]

Mitra, Quantum quench dynamics,Annu

A. Mitra, Quantum quench dynamics,Annu. Rev. Con- dens. Matter Phys.9, 245 (2018)

2018
[46]

Porta, F

S. Porta, F. Cavaliere, M. Sassetti, and N. Traverso Ziani, Topological classification of dynamical quantum phase transitions in the XY chain,Sci. Rep.10, 12766 (2020)

2020

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

Ezratty,Understanding Quantum Technologies (2024), arXiv:2111.15352 [quant-ph]

O. Ezratty,Understanding Quantum Technologies (2024), arXiv:2111.15352 [quant-ph]

arXiv 2024

[2] [2]

Aguado, R

R. Aguado, R. Citro, M. Lewenstein, and M. Stern,New Trends and Platforms for Quantum Technologies, Lecture 6 Notes in Physics Vol. 1025 (Springer Nature Switzerland, Cham, 2024)

2024

[3] [3]

J. Q. Quach, G. Cerullo, and T. Virgili, Quantum batter- ies: The future of energy storage?,Joule7, 2195 (2023)

2023

[4] [4]

Campaioli, S

F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries,Rev. Mod. Phys.96, 031001 (2024)

2024

[5] [5]

Camposeo, T

A. Camposeo, T. Virgili, F. Lombardi, G. Cerullo, D. Pisignano, and M. Polini, Quantum batteries: A materi- als science perspective,Adv. Mater.37, 2415073 (2025)

2025

[6] [6]

Ferraro, F

D. Ferraro, F. Cavaliere, M. G. Genoni, G. Benenti, and M. Sassetti, Opportunities and challenges of quantum batteries,Nat. Rev. Phys.(2026), doi:10.1038/s42254- 025-00906-5

doi:10.1038/s42254- 2026

[7] [7]

G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Charger-mediated energy transfer in exactly solvable models for quantum batteries, Phys. Rev. B98, 205423 (2018)

2018

[8] [8]

F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: Powerful charging of quantum batteries, New J. Phys.17, 075015 (2015)

2015