pith. sign in

arxiv: 2508.14847 · v2 · submitted 2025-08-20 · 🪐 quant-ph · cond-mat.other

Power-law-graded Ising Interactions Stabilize Time Crystals Realizing Quantum Energy Storage and Sensing

Ayan Sahoo , Debraj Rakshit This is my paper

Pith reviewed 2026-05-18 22:18 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.other
keywords discrete time crystalsFloquet drivingIsing interactionsquantum batteriesquantum Fisher informationpower-law interactionsStark localizationquantum sensing
0
0 comments X

The pith

Power-law-graded Ising interactions stabilize discrete time crystals enabling superlinear energy storage and superextensive quantum sensing.

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

The paper examines one-dimensional chains of spin-1/2 particles with interactions that vary as a power law across the chain. It shows that periodic driving can lock the system into a discrete time crystal phase over a broad range of how steeply the interactions fall off. In this phase the total energy that can be stored grows faster than the number of spins, and the precision for measuring small changes in the drive period improves faster than the usual quantum limit. This combination suggests the setup could serve as both a quantum battery and a sensitive clock.

Core claim

By generalizing Stark localization to power-law-graded Ising interaction profiles, robust period-doubled dynamics are identified across a wide range of interaction exponents in one-dimensional spin-1/2 chains under periodic Floquet driving. Within the DTC phase the stored energy increases superlinearly with system size while the quantum Fisher information for timing deviations scales superextensively and surpasses the Heisenberg limit, with the advantage tunable via the interaction exponent.

What carries the argument

The power-law-graded Ising interaction profile, which generalizes Stark localization by creating a spatially varying coupling that stabilizes period-doubled dynamics when combined with coherent periodic driving.

If this is right

  • The discrete time crystal phase remains stable for a wide range of power-law exponents.
  • Energy stored in the DTC phase grows superlinearly with the number of spins.
  • Normalized power shows no scaling advantage with system size.
  • Quantum Fisher information for estimating drive timing deviations scales superextensively with system size.
  • The quantum advantage in sensing can be adjusted by changing the interaction exponent while DTC behavior stays intact.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar spatially graded couplings might be engineered in trapped-ion or superconducting platforms to combine energy storage with metrological gain.
  • The superextensive scaling could appear in other Floquet systems once long-range or position-dependent interactions replace uniform ones.
  • Checking whether the same scalings survive in two-dimensional lattices would test if the advantage is tied to one-dimensional geometry.

Load-bearing premise

The generalization of Stark localization to power-law-graded Ising interaction profiles produces robust period-doubled dynamics across a wide range of interaction exponents through the interplay between coherent driving and spatially varying coupling.

What would settle it

Numerical simulation of the driven spin chain for interaction exponents spanning several decades showing that the period-doubled magnetization order parameter decays to zero after a few drive periods would disprove the claimed robustness of the DTC phase.

Figures

Figures reproduced from arXiv: 2508.14847 by Ayan Sahoo, Debraj Rakshit.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The schematic diagram illustrates the battery charging pro [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The scaling exponent of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The scaling exponent of QFI with system-size, [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We study discrete time-crystalline (DTC) phases in one-dimensional spin-1/2 chains with power-law-graded Ising interactions under periodic Floquet driving. By generalizing Stark localization to power-law-graded Ising interaction profiles, we identify robust period-doubled dynamics across a wide range of interaction exponents, stabilized by the interplay between coherent driving and spatially varying coupling. Within the DTC phase, the energy stored in the system, interpreted as a quantum battery, increases superlinearly with system size, although no scaling advantage persists in normalized power. Beyond energy storage, we demonstrate that the DTC phase supports enhanced quantum sensing. The quantum Fisher information associated with estimating timing deviations in the drive scales superextensively with system size, surpassing the Heisenberg limit. The degree of quantum advantage can be tuned by varying the interaction exponent, though DTC behavior remains robust throughout. Our results position power-law-graded Ising interacting Floquet systems as robust platforms for storing quantum energy and achieving metrological enhancement.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript examines discrete time-crystalline (DTC) phases in one-dimensional spin-1/2 chains with power-law-graded Ising interactions under periodic Floquet driving. It generalizes Stark localization to these spatially varying couplings and reports robust period-doubled dynamics over a wide range of interaction exponents. Within the DTC phase the stored energy (interpreted as a quantum battery) is claimed to scale superlinearly with system size, while the quantum Fisher information for estimating timing deviations in the drive scales superextensively and exceeds the Heisenberg limit; both advantages are said to be tunable by the exponent while DTC behavior remains stable.

Significance. If the reported scalings and robustness hold, the work identifies a tunable platform that combines DTC stability with practical quantum-battery and metrological advantages, potentially expanding the design space for Floquet-engineered devices beyond uniform or linearly graded interactions.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (scaling results): the claims of superlinear energy storage and superextensive QFI are stated without visible error bars, explicit system-size range, or exclusion criteria for the data points; this makes it impossible to rule out finite-size artifacts or post-hoc fitting as the source of the reported exponents.
  2. [§2.2 and §4] §2.2 and §4 (generalized Stark localization): the central claim that period-doubled dynamics remain robust for interaction exponents down to α ≲ 1 rests on the assumption that the effective localization length stays finite and protective against long-range dephasing; no explicit localization-length or heating-rate data are shown for this regime, which is load-bearing for the DTC phase, battery scaling, and QFI advantage.
minor comments (2)
  1. [Model definition] The precise functional form of the power-law-graded Ising term (e.g., the spatial dependence of the coupling strength) should be written as an explicit equation in the model section for reproducibility.
  2. [Figures] Figure captions for the scaling plots should state the fitting procedure and the number of disorder realizations used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting points that can improve the clarity and rigor of our presentation. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (scaling results): the claims of superlinear energy storage and superextensive QFI are stated without visible error bars, explicit system-size range, or exclusion criteria for the data points; this makes it impossible to rule out finite-size artifacts or post-hoc fitting as the source of the reported exponents.

    Authors: We agree that the scaling analysis in §3 would benefit from greater transparency. In the revised manuscript we will add error bars to the energy-storage and QFI scaling plots (obtained from ensemble averages over initial states or disorder realizations), explicitly report the system-size range used (N = 8 to N = 24), and describe the fitting window together with any exclusion criteria for small-N data. These additions will allow readers to assess the robustness of the reported exponents against finite-size effects. revision: yes

  2. Referee: [§2.2 and §4] §2.2 and §4 (generalized Stark localization): the central claim that period-doubled dynamics remain robust for interaction exponents down to α ≲ 1 rests on the assumption that the effective localization length stays finite and protective against long-range dephasing; no explicit localization-length or heating-rate data are shown for this regime, which is load-bearing for the DTC phase, battery scaling, and QFI advantage.

    Authors: We acknowledge that direct evidence of localization in the α ≲ 1 regime would strengthen the central claim. While the main text already demonstrates persistent period-doubled dynamics, we will add in the revision explicit plots of the effective localization length versus α (extracted from the participation ratio or inverse participation ratio of Floquet eigenstates) and estimates of the heating rate obtained from long-time stroboscopic evolution. These data will be placed in §2.2 and the supplement to confirm that localization remains protective down to the lowest exponents considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation of DTC robustness and scalings is self-contained

full rationale

The paper generalizes Stark localization to power-law-graded Ising profiles and identifies robust period-doubled dynamics, superlinear battery scaling, and superextensive QFI from the resulting DTC phase. No quoted steps reduce predictions to fitted parameters by construction, invoke load-bearing self-citations whose uniqueness is unverified, or smuggle ansatzes via prior work. The central claims follow from the stated interplay of coherent driving and spatially varying couplings rather than tautological redefinitions of the DTC phase or localization length. This matches the expected honest non-finding for a study whose results remain externally falsifiable via numerics or experiment.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the domain assumption that Stark localization generalizes directly to power-law profiles and on the numerical identification of the DTC phase; the interaction exponent is treated as a tunable parameter rather than a fitted constant.

free parameters (1)
  • interaction exponent
    Varied across a range to demonstrate robustness; not fitted to a target observable but used to scan the phase diagram.
axioms (2)
  • domain assumption Generalization of Stark localization applies to power-law-graded Ising interactions
    Invoked to explain the stabilization of period-doubled dynamics.
  • domain assumption Periodic Floquet driving combined with spatially varying couplings produces robust DTC order
    Core premise underlying both the energy-storage and sensing claims.

pith-pipeline@v0.9.0 · 5702 in / 1492 out tokens · 45253 ms · 2026-05-18T22:18:16.757486+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Localization from Infinitesimal Kinetic Grading: Finite-size Scaling, Kibble-Zurek Dynamics and Applications in Sensing

    cond-mat.quant-gas 2025-12 unverdicted novelty 7.0

    Power-law kinetic grading in a 1D lattice drives a localization transition at alpha equals zero with diverging length, enabling critical enhancement of quantum Fisher information for parameter estimation.

  2. Interplay of Nonstabilizerness and Ergotropy in Quantum Batteries

    quant-ph 2026-05 unverdicted novelty 6.0

    Ergotropy in the battery corresponds one-to-one with total nonstabilizerness under U(1)-symmetric charger-battery interactions, while maximum average charging power in Clifford evolution is achievable even with zero i...

  3. Journey in quantum metrology and sensing from foundations to applications: a review

    quant-ph 2026-05 unverdicted novelty 1.0

    A review summarizing foundations and applications of quantum metrology and sensing including estimation strategies and experimental platforms.

Reference graph

Works this paper leans on

89 extracted references · 89 canonical work pages · cited by 3 Pith papers · 1 internal anchor

  1. [1]

    Wilczek, Quantum time crystals, Phys

    F. Wilczek, Quantum time crystals, Phys. Rev. Lett. 109, 160401 (2012)

    work page 2012

  2. [2]

    Li, Z.-X

    T. Li, Z.-X. Gong, Z.-Q. Yin, H. T. Quan, X. Yin, P. Zhang, L.- M. Duan, and X. Zhang, Space-time crystals of trapped ions, Phys. Rev. Lett. 109, 163001 (2012)

    work page 2012

  3. [3]

    Wilczek, Superfluidity and space-time translation symmetry breaking, Phys

    F. Wilczek, Superfluidity and space-time translation symmetry breaking, Phys. Rev. Lett. 111, 250402 (2013)

    work page 2013

  4. [4]

    S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V . Khemani, C. von Keyser- lingk, N. Y . Yao, E. Demlerm, and M. D. Lukin, Observation of discrete time-crystalline order in a disordered dipolar many- body system, Nature 543, 221 (2017)

    work page 2017

  5. [5]

    Zhang, P

    J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vish- wanath, N. Y . Yao, and C. Monroe, Observation of a discrete time crystal, Nature 543, 217 (2017)

    work page 2017

  6. [6]

    Zhang, W

    X. Zhang, W. Jiang, J. Deng, K. Wang, J. Chen, P. Zhang, W. Ren, H. Dong, S. Xu, Y . Gao, F. Jin, X. Zhu, Q. Guo, H. Li, C. Song, A. V . Gorshkov, T. Iadecola, F. Liu, Z.-X. Gong, Z. Wang, D.-L. Deng, and H. Wang, Digital quantum simulation of floquet symmetry-protected topological phases, Nature 607, 468 (2022)

    work page 2022

  7. [7]

    Serbyn, Z

    M. Serbyn, Z. Papi´c, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states, Phys. Rev. Lett. 111, 127201 (2013)

    work page 2013

  8. [8]

    D. A. Huse, R. Nandkishore, and V . Oganesyan, Phenomenol- ogy of fully many-body-localized systems, Phys. Rev. B 90, 174202 (2014)

    work page 2014

  9. [9]

    Fleckenstein and M

    C. Fleckenstein and M. Bukov, Thermalization and prethermal- ization in periodically kicked quantum spin chains, Phys. Rev. B 103, 144307 (2021)

    work page 2021

  10. [10]

    W. W. Ho, T. Mori, D. A. Abanin, and E. G. Dalla Torre, Quan- tum and classical floquet prethermalization, Annals of Physics 454, 169297 (2023)

    work page 2023

  11. [11]

    Mishra, R

    U. Mishra, R. Prabhu, and D. Rakshit, Quantum correlations in periodically driven spin chains: Revivals and steady-state properties, Journal of Magnetism and Magnetic Materials 491, 165546 (2019)

    work page 2019

  12. [12]

    Khemani, A

    V . Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phase structure of driven quantum systems, Phys. Rev. Lett. 116, 250401 (2016)

    work page 2016

  13. [13]

    D. V . Else, B. Bauer, and C. Nayak, Floquet time crystals, Phys. Rev. Lett. 117, 090402 (2016)

    work page 2016

  14. [14]

    C. W. von Keyserlingk and S. L. Sondhi, Phase structure of one- dimensional interacting floquet systems. ii. symmetry-broken phases, Phys. Rev. B 93, 245146 (2016)

    work page 2016

  15. [15]

    Ponte, A

    P. Ponte, A. Chandran, Z. Papi´c, and D. A. Abanin, Periodically driven ergodic and many-body localized quantum systems, An- nals of Physics 353, 196–204 (2015)

    work page 2015

  16. [16]

    C. W. von Keyserlingk, V . Khemani, and S. L. Sondhi, Ab- solute stability and spatiotemporal long-range order in floquet systems, Phys. Rev. B 94, 085112 (2016)

    work page 2016

  17. [17]

    Carollo, K

    F. Carollo, K. Brandner, and I. Lesanovsky, Nonequilibrium many-body quantum engine driven by time-translation symme- try breaking, Phys. Rev. Lett. 125, 240602 (2020)

    work page 2020

  18. [18]

    R. W. Bomantara and J. Gong, Simulation of non-abelian braid- ing in majorana time crystals, Phys. Rev. Lett. 120, 230405 (2018)

    work page 2018

  19. [19]

    M. P. Estarellas1, T. Osada1, V . M. Bastidas, B. Renoust, K. Sanaka, W. J. Munro1, and K. Nemoto, Simulating com- plex quantum networks with time crystals, Science Advances 6, eaay8892 (2020)

    work page 2020

  20. [20]

    Iemini, R

    F. Iemini, R. Fazio, and A. Sanpera, Floquet time crystals as quantum sensors of ac fields, Phys. Rev. A 109, L050203 (2024)

    work page 2024

  21. [21]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Continuous sensing and parameter estimation with the boundary time crystal, Phys. Rev. Lett. 132, 050801 (2024)

    work page 2024

  22. [22]

    Liu, S.-X

    S. Liu, S.-X. Zhang, C.-Y . Hsieh, S. Zhang, and H. Yao, Dis- crete time crystal enabled by stark many-body localization, Phys. Rev. Lett. 130, 120403 (2023)

    work page 2023

  23. [23]

    Debnath, A

    A. Debnath, A. Sahoo, and D. Rakshit, Ongoing work, (2025)

    work page 2025

  24. [25]

    Yousefjani, K

    R. Yousefjani, K. Sacha, and A. Bayat, Discrete time crystal phase as a resource for quantum-enhanced sensing, Phys. Rev. B 111, 125159 (2025)

    work page 2025

  25. [26]

    A. R. Hogan and A. M. Martin, Quench dynamics in the jaynes-cummings-hubbard and dicke models, Physica Scripta 99, 055118 (2024)

    work page 2024

  26. [27]

    L. D. Marin Bukov and A. Polkovnikov, Universal high-frequency behavior of periodically driven sys- tems: from dynamical stabilization to floquet en- gineering, Advances in Physics 64, 139 (2015), https://doi.org/10.1080/00018732.2015.1055918

    work page doi:10.1080/00018732.2015.1055918 2015

  27. [28]

    Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev

    A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017)

    work page 2017

  28. [29]

    Alicki and M

    R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E 87, 042123 (2013)

    work page 2013

  29. [30]

    Ghosh and A

    S. Ghosh and A. Sen(De), Dimensional enhancements in a quantum battery with imperfections, Phys. Rev. A 105, 022628 (2022)

    work page 2022

  30. [31]

    Julià-Farré, T

    S. Julià-Farré, 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)

    work page 2020

  31. [32]

    Ferraro, M

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

    work page 2018

  32. [33]

    G. M. Andolina, M. Keck, A. Mari, V . Giovannetti, and M. Polini, Quantum versus classical many-body batteries, Phys. Rev. B 99, 205437 (2019)

    work page 2019

  33. [34]

    A. C. Santos, B. i. e. i. f. m. c. Çakmak, S. Campbell, and N. T. Zinner, Stable adiabatic quantum batteries, Phys. Rev. E 100, 032107 (2019)

    work page 2019

  34. [35]

    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)

    work page 2020

  35. [37]

    Crescente, M

    A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, Ultrafast charging in a two-photon dicke quantum battery, Phys. Rev. B 102, 245407 (2020)

    work page 2020

  36. [38]

    Crescente, D

    A. Crescente, D. Ferraro, M. Carrega, and M. Sassetti, Enhanc- ing coherent energy transfer between quantum devices via a me- diator, Phys. Rev. Res. 4, 033216 (2022)

    work page 2022

  37. [39]

    Ghosh, T

    S. Ghosh, T. Chanda, and A. Sen(De), Enhancement in the per- formance of a quantum battery by ordered and disordered inter- actions, Phys. Rev. A 101, 032115 (2020)

    work page 2020

  38. [40]

    Ghosh, T

    S. Ghosh, T. Chanda, S. Mal, and A. Sen(De), Fast charging of 12 a quantum battery assisted by noise, Phys. Rev. A 104, 032207 (2021)

    work page 2021

  39. [41]

    T. K. Konar, L. G. C. Lakkaraju, S. Ghosh, and A. Sen(De), Quantum battery with ultracold atoms: Bosons versus fermions, Phys. Rev. A 106, 022618 (2022)

    work page 2022

  40. [42]

    Bhattacharyya, K

    A. Bhattacharyya, K. Sen, and U. Sen, Noncompletely positive quantum maps enable efficient local energy extraction in batter- ies, Phys. Rev. Lett. 132, 240401 (2024)

    work page 2024

  41. [43]

    Sen and U

    K. Sen and U. Sen, Local passivity and entanglement in shared quantum batteries, Phys. Rev. A 104, L030402 (2021)

    work page 2021

  42. [44]

    Auxiliary-assisted stochastic energy extraction from quantum batteries,

    P. Chaki, A. Bhattacharyya, K. Sen, and U. Sen, Auxiliary- assisted stochastic energy extraction from quantum batteries, arXiv:2307.16856 (2023)

    work page arXiv 2023

  43. [45]

    Sen and U

    K. Sen and U. Sen, Noisy quantum batteries, arXiv:2302.07166 (2023)

    work page arXiv 2023

  44. [46]

    G. Zhu, Y . Chen, Y . Hasegawa, and P. Xue, Charging quantum batteries via indefinite causal order: Theory and experiment, Phys. Rev. Lett. 131, 240401 (2023)

    work page 2023

  45. [47]

    Rossini, G

    D. Rossini, G. M. Andolina, and M. Polini, Many-body local- ized quantum batteries, Phys. Rev. B 100, 115142 (2019)

    work page 2019

  46. [48]

    M. B. Arjmandi, H. Mohammadi, A. Saguia, M. S. Sarandy, and A. C. Santos, Localization effects in disordered quantum batteries, Phys. Rev. E 108, 064106 (2023)

    work page 2023

  47. [49]

    Mondal and S

    S. Mondal and S. Bhattacharjee, Periodically driven many-body quantum battery, Phys. Rev. E105, 044125 (2022)

    work page 2022

  48. [50]

    S. Puri, T. K. Konar, L. G. C. Lakkaraju, and A. S. De, Floquet driven long-range interactions induce super-extensive scaling in quantum battery, arXiv preprint arXiv:2412.00921 (2024)

    work page arXiv 2024

  49. [51]

    M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, and J. Za- krzewski, At the limits of criticality-based quantum metrology: Apparent super-heisenberg scaling revisited, Phys. Rev. X 8, 021022 (2018)

    work page 2018

  50. [52]

    Zanardi, M

    P. Zanardi, M. G. A. Paris, and L. Campos Venuti, Quantum criticality as a resource for quantum estimation, Phys. Rev. A 78, 042105 (2008)

    work page 2008

  51. [53]

    Campos Venuti and P

    L. Campos Venuti and P. Zanardi, Quantum critical scaling of the geometric tensors, Phys. Rev. Lett. 99, 095701 (2007)

    work page 2007

  52. [54]

    Tsang, Quantum transition-edge detectors, Phys

    M. Tsang, Quantum transition-edge detectors, Phys. Rev. A 88, 021801 (2013)

    work page 2013

  53. [55]

    Garbe, M

    L. Garbe, M. Bina, A. Keller, M. G. A. Paris, and S. Felicetti, Critical quantum metrology with a finite-component quantum phase transition, Phys. Rev. Lett. 124, 120504 (2020)

    work page 2020

  54. [56]

    Y . Chu, S. Zhang, B. Yu, and J. Cai, Dynamic framework for criticality-enhanced quantum sensing, Phys. Rev. Lett. 126, 010502 (2021)

    work page 2021

  55. [57]

    Montenegro, U

    V . Montenegro, U. Mishra, and A. Bayat, Global sensing and its impact for quantum many-body probes with criticality, Phys. Rev. Lett. 126, 200501 (2021)

    work page 2021

  56. [58]

    S. S. Mirkhalaf, E. Witkowska, and L. Lepori, Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate, Phys. Rev. A 101, 043609 (2020)

    work page 2020

  57. [59]

    Frérot and T

    I. Frérot and T. Roscilde, Quantum critical metrology, Phys. Rev. Lett. 121, 020402 (2018)

    work page 2018

  58. [60]

    Zanardi and N

    P. Zanardi and N. Paunkovi´c, Ground state overlap and quantum phase transitions, Phys. Rev. E 74, 031123 (2006)

    work page 2006

  59. [61]

    You, Y .-W

    W.-L. You, Y .-W. Li, and S.-J. Gu, Fidelity, dynamic structure factor, and susceptibility in critical phenomena, Phys. Rev. E 76, 022101 (2007)

    work page 2007

  60. [62]

    Zanardi, P

    P. Zanardi, P. Giorda, and M. Cozzini, Information-theoretic differential geometry of quantum phase transitions, Phys. Rev. Lett. 99, 100603 (2007)

    work page 2007

  61. [63]

    Ilias, D

    T. Ilias, D. Yang, S. F. Huelga, and M. B. Plenio, Criticality- enhanced quantum sensing via continuous measurement, PRX Quantum 3, 010354 (2022)

    work page 2022

  62. [64]

    Gietka, F

    K. Gietka, F. Metz, T. Keller, and J. Li, Adiabatic critical quan- tum metrology cannot reach the heisenberg limit even when shortcuts to adiabaticity are applied, Quantum 5, 489 (2021)

    work page 2021

  63. [65]

    GU, Fidelity approach to quantum phase transitions, Inter- national Journal of Modern Physics B 24, 4371–4458 (2010)

    S.-J. GU, Fidelity approach to quantum phase transitions, Inter- national Journal of Modern Physics B 24, 4371–4458 (2010)

    work page 2010

  64. [66]

    Mondal, A

    S. Mondal, A. Sahoo, U. Sen, and D. Rakshit, Mul- ticritical quantum sensors driven by symmetry-breaking, arXiv:2407.14428 (2024)

    work page arXiv 2024

  65. [67]

    K. D. Agarwal, T. K. Konar, L. G. C. Lakkaraju, and A. S. De, Critical quantum metrology using non-hermitian spin model with rt-symmetry, arXiv:2503.24331 (2025)

    work page arXiv 2025

  66. [68]

    Mishra and A

    U. Mishra and A. Bayat, Driving enhanced quantum sensing in partially accessible many-body systems, Phys. Rev. Lett. 127, 080504 (2021)

    work page 2021

  67. [69]

    Mishra and A

    U. Mishra and A. Bayat, Integrable quantum many-body sen- sors for ac field sensing, Scientific Reports 12 (2022)

    work page 2022

  68. [70]

    Dooley, Robust quantum sensing in strongly interacting sys- tems with many-body scars, PRX Quantum 2, 020330 (2021)

    S. Dooley, Robust quantum sensing in strongly interacting sys- tems with many-body scars, PRX Quantum 2, 020330 (2021)

    work page 2021

  69. [71]

    Desaules, F

    J.-Y . Desaules, F. Pietracaprina, Z. Papi´c, J. Goold, and S. Pap- palardi, Extensive multipartite entanglement from su(2) quan- tum many-body scars, Phys. Rev. Lett. 129, 020601 (2022)

    work page 2022

  70. [72]

    Dooley, S

    S. Dooley, S. Pappalardi, and J. Goold, Entanglement enhanced metrology with quantum many-body scars, Phys. Rev. B 107, 035123 (2023)

    work page 2023

  71. [73]

    Z. Guo, B. Liu, Y . Gao, A. Yang, J. Wang, J. Ma, and L. Ying, Origin of hilbert-space quantum scars in unconstrained models, Phys. Rev. B 108, 075124 (2023)

    work page 2023

  72. [74]

    X. He, R. Yousefjani, and A. Bayat, Stark localization as a re- source for weak-field sensing with super-heisenberg precision, Phys. Rev. Lett. 131, 010801 (2023)

    work page 2023

  73. [75]

    Sahoo, U

    A. Sahoo, U. Mishra, and D. Rakshit, Localization-driven quan- tum sensing, Phys. Rev. A 109, L030601 (2024)

    work page 2024

  74. [76]

    Sahoo and D

    A. Sahoo and D. Rakshit, Enhanced sensing of stark weak field under the influence of aubry-andr {\’e}-harper criticality, arXiv:2408.03232 (2024)

    work page arXiv 2024

  75. [77]

    Sahoo, A

    A. Sahoo, A. Saha, and D. Rakshit, Stark localization near aubry-andré criticality, Phys. Rev. B111, 024205 (2025)

    work page 2025

  76. [78]

    Tilt-Induced Localization in Interacting Bose-Einstein Condensates for Quantum Sensing

    A. Debnath, M. Gajda, and D. Rakshit, Tilt-induced localization in interacting bose-einstein condensates for quantum sensing, arXiv:2506.06173 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  77. [79]

    Montenegro, C

    V . Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Review: Quantum metrology and sensing with many-body systems, Physics Re- ports 1134, 1–62 (2025)

    work page 2025

  78. [80]

    K. D. Agarwal, S. Mondal, A. Sahoo, D. Rakshit, A. S. De, and U. Sen, Quantum sensing with ultracold simulators in lattice and ensemble systems: a review, arXiv:2507.06348 (2025)

    work page arXiv 2025

  79. [81]

    Montenegro, M

    V . Montenegro, M. G. Genoni, A. Bayat, and M. G. A. Paris, Quantum metrology with boundary time crystals, Communica- tions Physics 6 (2023)

    work page 2023

  80. [82]

    Biswas and S

    H. Biswas and S. Choudhury, Discrete time crystals in the spin- s central spin model, arXiv:2505.13207 (2025)

    work page arXiv 2025

Showing first 80 references.