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arxiv: 2604.09892 · v1 · submitted 2026-04-10 · 🪐 quant-ph · cond-mat.mes-hall

Enhanced dissipative criticality at an exceptional point

Jongjun M. Lee This is my paper

Pith reviewed 2026-05-10 17:01 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords exceptional pointsdissipative phase transitionsopen Dicke modelcritical fluctuationsJordan-block dynamicsnon-Hermitian physicsquantum sensing
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0 comments X

The pith

When an exceptional point coincides with a dissipative phase transition in an open Dicke model, critical fluctuations amplify and follow modified scaling exponents.

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

The paper studies an extended open Dicke model with two cavities coupled to a collective spin. It finds that tuning an exceptional point to coincide with the dissipative phase transition strongly amplifies critical fluctuations and changes their scaling exponents. This holds in both the normal and superradiant phases according to numerical results and an analytical treatment based on Jordan-block dynamics. A reader would care because the result supplies a concrete route to control criticality in open quantum systems.

Core claim

In the extended open Dicke model of two cavities coupled to a collective spin, when an exceptional point coincides with the dissipative phase transition, the critical fluctuations are strongly amplified and governed by modified critical exponents. Numerical simulations confirm enhanced scaling in both phases, matching an analytical theory that attributes the change to the Jordan-block structure induced by the exceptional point.

What carries the argument

The Jordan-block dynamics that arises when eigenvalues and eigenvectors coalesce at the exceptional point tuned to the phase transition.

If this is right

  • Enhanced critical scaling appears numerically in both the normal and superradiant phases.
  • The analytical theory based on EP-induced Jordan-block dynamics reproduces the numerical scaling.
  • Exceptional points act as a controllable mechanism for engineering critical scaling in open quantum systems.
  • The setup suggests applications to critical quantum sensing.

Where Pith is reading between the lines

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

  • The same coincidence of exceptional point and transition could be attempted in other open quantum models to test whether fluctuation amplification is general.
  • Cavity-QED experiments could directly measure the modified exponents to confirm the Jordan-block prediction.
  • Engineering stronger criticality this way might improve the sensitivity of sensors that operate near phase transitions.

Load-bearing premise

The exceptional point can be tuned to coincide exactly with the dissipative phase transition so that its Jordan-block dynamics controls the fluctuations without other effects dominating.

What would settle it

Numerical or experimental data showing that the critical exponents near the transition remain unchanged from the standard dissipative values, rather than matching the modified ones predicted by the Jordan-block analysis.

Figures

Figures reproduced from arXiv: 2604.09892 by Jongjun M. Lee.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustrations of (a) the extended open Dicke [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Static Gaussian observables as functions of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Noise spectrum near and at the critical point. (a,b) Noise spectrum ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Liouvillian spectrum near the critical point [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
read the original abstract

Exceptional points (EPs) represent non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to enhanced sensitivity and critically damped dynamics. We demonstrate that when an EP coincides with a dissipative phase transition in an extended open Dicke model of two cavities coupled to a collective spin, the critical fluctuations are strongly amplified and governed by modified critical exponents. Numerical results reveal enhanced critical scaling in both the normal and superradiant phases, in agreement with an analytical theory based on EP-induced Jordan-block dynamics. Our results establish EPs as a mechanism to engineer critical scaling in open quantum systems, with potential applications to critical quantum sensing.

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

0 major / 3 minor

Summary. The paper studies an extended open Dicke model with two cavities coupled to a collective spin. It claims that when an exceptional point (EP) is tuned to coincide with a dissipative phase transition, critical fluctuations are strongly amplified and obey modified critical exponents. Numerical simulations show enhanced scaling in both the normal and superradiant phases, and these results are stated to agree with an analytical derivation based on the Jordan-block structure induced by the EP. The work positions EPs as a tool to engineer critical scaling in open quantum systems, with suggested applications to critical quantum sensing.

Significance. If the central claim holds, the manuscript identifies a concrete mechanism for amplifying and modifying critical fluctuations in open quantum systems by aligning an EP with a dissipative transition. The combination of numerical scaling data with an analytical Jordan-block treatment is a positive feature, as it supplies both empirical support and a dynamical explanation. The use of the well-studied Dicke model increases accessibility and relevance to ongoing work on non-Hermitian open systems and quantum sensing.

minor comments (3)
  1. The abstract and introduction would benefit from an explicit statement of the modified critical exponents (rather than only describing them as 'modified') so that readers can immediately compare with standard mean-field or dissipative exponents.
  2. In the section presenting the analytical theory, the mapping from the EP-induced Jordan block to the modified scaling should include a brief derivation of the exponent shift, including any assumptions about the dominant slow mode.
  3. Figure captions for the scaling plots should specify the system sizes, fitting ranges, and how finite-size effects were controlled when extracting the numerical exponents.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading, accurate summary of our results, and recommendation for minor revision. We are pleased that the positive significance of aligning an exceptional point with a dissipative phase transition to amplify critical fluctuations is recognized, along with the value of combining numerical scaling data and the analytical Jordan-block treatment in the extended open Dicke model.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's central result—that critical fluctuations are amplified with modified exponents when an EP coincides with a dissipative phase transition—rests on numerical scaling in the extended open Dicke model together with an analytical derivation explicitly based on standard EP-induced Jordan-block dynamics. This analytical component is described as independent and drawn from established non-Hermitian physics rather than being fitted to the target critical data or defined in terms of the claimed exponents. No load-bearing self-citations, self-definitional steps, or smuggled ansatzes are indicated; the model construction that permits EP-phase-transition coincidence is presented as a tunable feature, not a circular premise. The derivation is therefore self-contained against external benchmarks of EP theory and open-system criticality.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work relies on standard non-Hermitian and open-system concepts without introducing new free parameters or invented entities.

axioms (1)
  • domain assumption Standard assumptions of non-Hermitian quantum mechanics and Lindblad dynamics for open systems.
    The model and EP analysis presuppose these established frameworks.

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Works this paper leans on

59 extracted references · 59 canonical work pages · cited by 1 Pith paper

  1. [1]

    S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Continuous quantum phase transitions, Rev. Mod. Phys. 69, 315 (1997)

    work page 1997

  2. [2]

    Sachdev,Quantum Phase Transitions, 2nd ed

    S. Sachdev,Quantum Phase Transitions, 2nd ed. (Cam- bridge University Press, 2011)

    work page 2011

  3. [3]

    Diehl, A

    S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. B¨ uchler, and P. Zoller, Quantum states and phases in driven open quantum systems with cold atoms, Nature Physics4, 878 (2008)

    work page 2008

  4. [4]

    E. M. Kessler, G. Giedke, A. Imamoglu, S. F. Yelin, M. D. Lukin, and J. I. Cirac, Dissipative phase transition in a central spin system, Phys. Rev. A86, 012116 (2012)

    work page 2012

  5. [5]

    H. J. Carmichael, Breakdown of photon blockade: A dis- sipative quantum phase transition in zero dimensions, Phys. Rev. X5, 031028 (2015)

    work page 2015

  6. [6]

    L. M. Sieberer, M. Buchhold, and S. Diehl, Keldysh field theory for driven open quantum systems, Reports on Progress in Physics79, 096001 (2016)

    work page 2016

  7. [7]

    Minganti, A

    F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spec- tral theory of liouvillians for dissipative phase transitions, Phys. Rev. A98, 042118 (2018)

    work page 2018

  8. [8]

    Fazio, J

    R. Fazio, J. Keeling, L. Mazza, and M. Schir` o, Many- body open quantum systems, SciPost Phys. Lect. Notes , 99 (2025)

    work page 2025

  9. [9]

    S. R. K. Rodriguez, W. Casteels, F. Storme, N. Car- lon Zambon, I. Sagnes, L. Le Gratiet, E. Galopin, 6 A. Lemaˆ ıtre, A. Amo, C. Ciuti, and J. Bloch, Probing a dissipative phase transition via dynamical optical hys- teresis, Phys. Rev. Lett.118, 247402 (2017)

    work page 2017

  10. [10]

    Fitzpatrick, N

    M. Fitzpatrick, N. M. Sundaresan, A. C. Y. Li, J. Koch, and A. A. Houck, Observation of a dissipative phase tran- sition in a one-dimensional circuit qed lattice, Phys. Rev. X7, 011016 (2017)

    work page 2017

  11. [11]

    T. Fink, A. Schade, S. H¨ ofling, C. Schneider, and A. Imamoglu, Signatures of a dissipative phase transition in photon correlation measurements, Nature Physics14, 365 (2018)

    work page 2018

  12. [12]

    Brookes, G

    P. Brookes, G. Tancredi, A. D. Patterson, J. Rahamim, M. Esposito, T. K. Mavrogordatos, P. J. Leek, E. Gi- nossar, and M. H. Szymanska, Critical slowing down in circuit quantum electrodynamics, Science advances7, eabe9492 (2021)

    work page 2021

  13. [13]

    Diehl, A

    S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, Dynamical phase transitions and instabilities in open atomic many-body systems, Phys. Rev. Lett.105, 015702 (2010)

    work page 2010

  14. [14]

    Marino and S

    J. Marino and S. Diehl, Quantum dynamical field the- ory for nonequilibrium phase transitions in driven open systems, Phys. Rev. B94, 085150 (2016)

    work page 2016

  15. [15]

    Hwang, P

    M.-J. Hwang, P. Rabl, and M. B. Plenio, Dissipative phase transition in the open quantum rabi model, Phys. Rev. A97, 013825 (2018)

    work page 2018

  16. [16]

    Belyansky, C

    R. Belyansky, C. Weis, R. Hanai, P. B. Littlewood, and A. A. Clerk, Phase transitions in nonreciprocal driven- dissipative condensates, Phys. Rev. Lett.135, 123401 (2025)

    work page 2025

  17. [17]

    L. M. Sieberer, M. Buchhold, J. Marino, and S. Diehl, Universality in driven open quantum matter, Rev. Mod. Phys.97, 025004 (2025)

    work page 2025

  18. [18]

    J. M. Lee, M.-J. Hwang, and I. Boettcher, Universal- ity classes split by strong and weak symmetries (2026), arXiv:2602.09090 [quant-ph]

    work page arXiv 2026

  19. [19]

    Minganti, A

    F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-hermitian hamiltonians and liouvillians: The effects of quantum jumps, Phys. Rev. A100, 062131 (2019)

    work page 2019

  20. [20]

    Khandelwal, N

    S. Khandelwal, N. Brunner, and G. Haack, Signatures of liouvillian exceptional points in a quantum thermal machine, PRX Quantum2, 040346 (2021)

    work page 2021

  21. [21]

    Zhou, X.-D

    Y.-L. Zhou, X.-D. Yu, C.-W. Wu, X.-Q. Li, J. Zhang, W. Li, and P.-X. Chen, Accelerating relaxation through liouvillian exceptional point, Phys. Rev. Res.5, 043036 (2023)

    work page 2023

  22. [22]

    El-Ganainy, K

    R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non- hermitian physics and pt symmetry, Nature Physics14, 11 (2018)

    work page 2018

  23. [23]

    I. I. Arkhipov, A. Miranowicz, F. Minganti, and F. Nori, Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switch- ing betweenPTand anti-PTsymmetries, Phys. Rev. A 102, 033715 (2020)

    work page 2020

  24. [24]

    Wiersig, Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle de- tection, Phys

    J. Wiersig, Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle de- tection, Phys. Rev. Lett.112, 203901 (2014)

    work page 2014

  25. [25]

    Wiersig, Sensors operating at exceptional points: Gen- eral theory, Phys

    J. Wiersig, Sensors operating at exceptional points: Gen- eral theory, Phys. Rev. A93, 033809 (2016)

    work page 2016

  26. [26]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Kha- javikhan, Enhanced sensitivity at higher-order excep- tional points, Nature548, 187 (2017)

    work page 2017

  27. [27]

    Chen, S ¸

    W. Chen, S ¸. Kaya ¨Ozdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature548, 192 (2017)

    work page 2017

  28. [28]

    W. Mao, Z. Fu, Y. Li, F. Li, and L. Yang, Exceptional– point–enhanced phase sensing, Science Advances10, eadl5037 (2024)

    work page 2024

  29. [29]

    T. Gao, E. Estrecho, K. Bliokh, T. Liew, M. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. H¨ ofling, Y. Ya- mamoto,et al., Observation of non-hermitian degenera- cies in a chaotic exciton-polariton billiard, Nature526, 554 (2015)

    work page 2015

  30. [30]

    Zhang, B

    J. Zhang, B. Peng, S ¸. K. ¨Ozdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y.-x. Liu, S. Rotter, and L. Yang, A phonon laser operating at an exceptional point, Nature Photonics12, 479 (2018)

    work page 2018

  31. [31]

    H.-Z. Chen, T. Liu, H.-Y. Luan, R.-J. Liu, X.-Y. Wang, X.-F. Zhu, Y.-B. Li, Z.-M. Gu, S.-J. Liang, H. Gao,et al., Revealing the missing dimension at an exceptional point, Nature Physics16, 571 (2020)

    work page 2020

  32. [32]

    C. Wang, J. Rao, Z. Chen, K. Zhao, L. Sun, B. Yao, T. Yu, Y.-P. Wang, and W. Lu, Enhancement of magnonic frequency combs by exceptional points, Nature Physics20, 1139 (2024)

    work page 2024

  33. [33]

    R. H. Dicke, Coherence in spontaneous radiation pro- cesses, Phys. Rev.93, 99 (1954)

    work page 1954

  34. [34]

    Hepp and E

    K. Hepp and E. H. Lieb, Equilibrium statistical mechan- ics of matter interacting with the quantized radiation field, Phys. Rev. A8, 2517 (1973)

    work page 1973

  35. [35]

    Kirton, M

    P. Kirton, M. M. Roses, J. Keeling, and E. G. Dalla Torre, Introduction to the Dicke model: From equilibrium to nonequilibrium, and vice versa, Advanced Quantum Technologies2, 1800043 (2019)

    work page 2019

  36. [36]

    D. Nagy, G. Szirmai, and P. Domokos, Critical exponent of a quantum-noise-driven phase transition: The open- system dicke model, Physical Review A—Atomic, Molec- ular, and Optical Physics84, 043637 (2011)

    work page 2011

  37. [37]

    E. G. D. Torre, S. Diehl, M. D. Lukin, S. Sachdev, and P. Strack, Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities, Phys. Rev. A87, 023831 (2013)

    work page 2013

  38. [38]

    Kirton and J

    P. Kirton and J. Keeling, Suppressing and restoring the dicke superradiance transition by dephasing and decay, Phys. Rev. Lett.118, 123602 (2017)

    work page 2017

  39. [39]

    W. D. Heiss, The physics of exceptional points, Journal of Physics A: Mathematical and Theoretical45, 444016 (2012)

    work page 2012

  40. [40]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Non-hermitian physics, Advances in Physics69, 249 (2020)

    work page 2020

  41. [41]

    Y. Xing, X. Zhao, H. Jing, and S.-L. Su, Exceptional- point dynamics (2025), arXiv:2507.14892 [quant-ph]

    work page arXiv 2025

  42. [42]

    L. D. Landau and E. M. Lifshitz,Mechanics, 3rd ed., Course of Theoretical Physics, Vol. 1 (Butterworth- Heinemann, Oxford, 1976)

    work page 1976

  43. [43]

    Lelas, N

    K. Lelas, N. Poljak, and D. Juki´ c, Damped harmonic os- cillator revisited: the fastest route to equilibrium, Amer- ican journal of physics91, 767 (2023)

    work page 2023

  44. [44]

    Buˇ ca and T

    B. Buˇ ca and T. Prosen, A note on symmetry reductions of the lindblad equation: transport in constrained open spin chains, New Journal of Physics14, 073007 (2012)

    work page 2012

  45. [45]

    V. V. Albert and L. Jiang, Symmetries and conserved quantities in lindblad master equations, Phys. Rev. A 7 89, 022118 (2014)

    work page 2014

  46. [46]

    S. Lieu, R. Belyansky, J. T. Young, R. Lundgren, V. V. Albert, and A. V. Gorshkov, Symmetry breaking and er- ror correction in open quantum systems, Phys. Rev. Lett. 125, 240405 (2020)

    work page 2020

  47. [47]

    See End Matter for further details

    work page

  48. [48]

    See the Supplemental Material for further details, in- cluding detailed calculations, additional data, and re- sults [49, 50]

    work page

  49. [49]

    Mari and J

    A. Mari and J. Eisert, Cooling by heating: Very hot ther- mal light can significantly cool quantum systems, Physi- cal review letters108, 120602 (2012)

    work page 2012

  50. [51]

    A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys.82, 1155 (2010)

    work page 2010

  51. [52]

    Mandal and E

    I. Mandal and E. J. Bergholtz, Symmetry and higher- order exceptional points, Phys. Rev. Lett.127, 186601 (2021)

    work page 2021

  52. [53]

    Schnabel, H

    J. Schnabel, H. Cartarius, J. Main, G. Wunner, and W. D. Heiss,PT-symmetric waveguide system with ev- idence of a third-order exceptional point, Phys. Rev. A 95, 053868 (2017)

    work page 2017

  53. [54]

    Zhang and J

    G.-Q. Zhang and J. Q. You, Higher-order exceptional point in a cavity magnonics system, Phys. Rev. B99, 054404 (2019)

    work page 2019

  54. [55]

    J. Kim, T. Ha, D. Kim, D. Lee, K.-S. Lee, J. Won, Y. Moon, and M. Lee, Third-order exceptional point in an ion–cavity system, Applied Physics Letters123, 10.1063/5.0168372 (2023)

    work page doi:10.1063/5.0168372 2023

  55. [56]

    Morrison and A

    S. Morrison and A. Parkins, Dissipation-driven quantum phase transitions in collective spin systems, Journal of Physics B: Atomic, Molecular and Optical Physics41, 195502 (2008)

    work page 2008

  56. [57]

    G. Lyu, K. Kottmann, M. B. Plenio, and M.-J. Hwang, Multicritical dissipative phase transitions in the anisotropic open quantum rabi model, Phys. Rev. Res. 6, 033075 (2024)

    work page 2024

  57. [58]

    Enhanced dissipative criticality at an exceptional point

    T. Holstein and H. Primakoff, Field dependence of the in- trinsic domain magnetization of a ferromagnet, Physical Review58, 1098 (1940). End Matter Equations of motion for the first moments.—From the Lindblad master equation, the equations of motion for the first moments are obtained as d⟨O⟩ dt = Tr[OL[ρ]],(29) whereO=a i, J j withi= 1,2 andj=x, y, z. Def...

    work page arXiv 1940

  58. [59]

    Mari and J

    A. Mari and J. Eisert, Cooling by heating: Very hot thermal light can significantly cool quantum systems, Physical review letters108, 120602 (2012)

    work page 2012

  59. [60]

    Woolley and A

    M. Woolley and A. Clerk, Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir, Physical Review A89, 063805 (2014)

    work page 2014