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arxiv: 2604.21820 · v1 · submitted 2026-04-23 · 🪐 quant-ph · cond-mat.quant-gas

Robust continuous symmetry breaking and multiversality in the chiral Dicke model

Nikolay Yegovtsev , Sayan Choudhury , W. Vincent Liu This is my paper

Pith reviewed 2026-05-09 22:18 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gas
keywords chiral Dicke modelU(1) symmetry breakingmultiversalitysuperradiant phasequantum phase transitionscritical exponentslight-matter couplingcavity QED
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The pith

Chiral interactions in the Dicke model enable robust continuous symmetry breaking and multiversality in quantum critical phenomena.

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

The authors generalize the standard Dicke model by incorporating chiral coupling of an atomic ensemble to a two-mode cavity field. This chiral coupling introduces a continuous U(1) symmetry linked to angular momentum. The ground-state phase diagram reveals a superradiant phase where this symmetry is broken over a wide range of parameters. Fluctuation spectra turn out to be tunable, and the transition between normal and superradiant phases displays multiversality, meaning the same phases are connected by critical points belonging to different universality classes, with the dynamical critical exponent product changing from one to one-half along a particular line.

Core claim

The chiral Dicke model possesses an inherent continuous U(1) symmetry due to its chiral light-matter interactions. Its ground state features a superradiant phase in which this U(1) symmetry is spontaneously broken. The quantum phase transition separating the normal phase from this superradiant phase belongs to different universality classes for different parameter values; specifically, the product of the dynamical critical exponent and the correlation-length exponent equals 1 along generic lines but equals 1/2 along a special line in parameter space.

What carries the argument

Chiral coupling to a two-mode cavity that conserves angular momentum and thereby imposes U(1) symmetry on the collective light-matter system.

If this is right

  • The U(1)-broken superradiant phase extends across a broad region of parameter space.
  • The spectrum of quantum fluctuations can be tuned independently in the symmetric and symmetry-broken phases.
  • Distinct universality classes govern the normal-superradiant transition depending on the path taken through parameter space.
  • The dynamical critical exponent product zν can be switched between 1 and 1/2 by choosing a special line.

Where Pith is reading between the lines

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

  • If realized experimentally, the model could allow controlled switching between different critical behaviors in the same physical system.
  • Multiversality may appear in other cavity QED setups that preserve continuous symmetries through chiral or similar interactions.
  • The tunability of fluctuations suggests potential for engineering quantum critical points with desired exponents for applications in quantum information or sensing.

Load-bearing premise

Mean-field theory and quadratic fluctuation analyses suffice to determine the phase boundaries and the values of the critical exponents without significant modifications from higher-order terms.

What would settle it

An experimental realization of the chiral Dicke model in which the measured dynamical critical exponent product for the normal-superradiant transition along the special line deviates from 1/2 would falsify the reported multiversality.

Figures

Figures reproduced from arXiv: 2604.21820 by Nikolay Yegovtsev, Sayan Choudhury, W. Vincent Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. (Left: A schematic illustration of chiral Dicke model [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy spectrum of Gaussian fluctuations above the mean-field ground state across different cuts through the phase [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The energy branches for the case [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous $U(1)$ symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a $U(1)$-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from $z\nu=1$ to $z\nu=1/2$. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.

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

1 major / 2 minor

Summary. The paper introduces the chiral Dicke model, a generalization of the standard Dicke model incorporating chiral light-matter couplings to a two-mode cavity that endows the system with a continuous U(1) symmetry tied to angular momentum conservation. It charts the ground-state phase diagram, identifies a broad U(1)-broken superradiant phase, and analyzes the spectrum of quantum fluctuations. The central claim is the existence of multiversality: the normal-superradiant quantum phase transition belongs to distinct universality classes depending on the path in parameter space, with the dynamical critical exponent changing from zν=1 to zν=1/2 along a special line.

Significance. If the multiversality result holds, the work would be significant for cavity QED and quantum many-body physics by providing a concrete, tunable platform realizing path-dependent universality classes in a U(1)-symmetric light-matter system. This extends the paradigm of the Dicke model and could inform experiments on collective excitations and Goldstone modes. The analytical charting of the phase diagram and fluctuation spectra via mean-field and quadratic methods is a clear strength, offering falsifiable predictions for critical exponents that can be tested in circuit QED or atomic ensembles.

major comments (1)
  1. [§3.2, Eq. (14)] §3.2, Eq. (14): The extraction of zν=1/2 along the special line is obtained from the gap closing and dispersion in the quadratic fluctuation Hamiltonian (via displacement and Bogoliubov diagonalization). However, when the quadratic coefficient is tuned to zero on this line, the chiral interaction terms generate anharmonic (cubic/quartic) contributions whose relevance under RG flow is not analyzed. These terms could drive the system away from the reported fixed point, undermining the claim that distinct universality classes govern the same transition.
minor comments (2)
  1. [Figure 2] Figure 2: The phase boundaries lack indication of whether they are obtained analytically or numerically, and the color bar for the order parameter is unlabeled.
  2. [Abstract] The abstract states results without referencing the specific method (mean-field plus quadratic fluctuations) used to obtain zν values; this should be clarified in the introduction for accessibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for identifying this important technical point regarding the analysis along the special line. We address the comment below and outline the changes we will make.

read point-by-point responses

  1. Referee: [§3.2, Eq. (14)] §3.2, Eq. (14): The extraction of zν=1/2 along the special line is obtained from the gap closing and dispersion in the quadratic fluctuation Hamiltonian (via displacement and Bogoliubov diagonalization). However, when the quadratic coefficient is tuned to zero on this line, the chiral interaction terms generate anharmonic (cubic/quartic) contributions whose relevance under RG flow is not analyzed. These terms could drive the system away from the reported fixed point, undermining the claim that distinct universality classes govern the same transition.

    Authors: We agree that a dedicated renormalization-group analysis of the anharmonic terms generated by the chiral couplings is absent from the manuscript. Our extraction of zν = 1/2 follows directly from the vanishing of the quadratic coefficient in the fluctuation Hamiltonian and the resulting dispersion of the soft mode. Because the U(1) symmetry forbids relevant cubic terms and the quartic terms are marginal or irrelevant at the Gaussian fixed point in the appropriate dimensionality, we expect the quadratic result to remain robust. Nevertheless, to address the referee’s concern rigorously we will add a short subsection (or appendix) that performs a power-counting analysis of the leading anharmonic operators and confirms their irrelevance. This will be included in the revised manuscript. revision: partial

Circularity Check

0 steps flagged

No circularity; multiversality extracted from explicit fluctuation spectrum

full rationale

The derivation begins from the chiral Dicke Hamiltonian, applies mean-field theory to locate the normal-superradiant transition, then diagonalizes the quadratic fluctuation Hamiltonian (via Holstein-Primakoff or Bogoliubov) to obtain the low-energy spectrum and extract path-dependent zν values. These steps are direct computations from the model parameters; no fitted quantities are relabeled as predictions, no self-citation supplies a uniqueness theorem that forces the result, and the reported change from zν=1 to zν=1/2 along a special line follows from the vanishing of a quadratic coefficient in the dispersion without circular redefinition. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the definition of chiral couplings in the Hamiltonian and on the validity of the fluctuation analysis used to extract critical exponents; no explicit free parameters or invented entities are named in the abstract.

free parameters (1)
  • chiral coupling parameters
    The model is defined by varying coupling strengths that control the phase diagram and the location of the special line where zν changes.
axioms (1)
  • domain assumption The introduced chiral interactions preserve a continuous U(1) symmetry associated with angular momentum conservation.
    Stated as an inherent property of the chiral Dicke model in the abstract.

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Reference graph

Works this paper leans on

82 extracted references · 6 canonical work pages · 1 internal anchor

  1. [1]

    =ω z|α3|2 −(g 2 1 +g 2

  2. [2]

    |α3|2(N− |α 3|2) N(˜ωc +U|α 3|2) .(3) We perform our computations in the regime 4ω2 c > U 2N2 to ensure that the ground state energy is a bounded con- tinuous function for the physically admissible values of |α3|< N. We now perform a further minimization procedure with respect toα ∗ 3 that yields two solutions, one cor- responding to the normal state (α 3...

  3. [3]

    Defenu, A

    N. Defenu, A. Lerose, and S. Pappalardi, Out-of- equilibrium dynamics of quantum many-body systems 5 with long-range interactions, Physics Reports1074, 1 (2024)

    2024

  4. [4]

    Defenu, T

    N. Defenu, T. Donner, T. Macr` ı, G. Pagano, S. Ruffo, and A. Trombettoni, Long-range interacting quantum systems, Rev. Mod. Phys.95, 035002 (2023)

    2023

  5. [5]

    Sinha, S

    S. Sinha, S. Ray, and S. Sinha, Classical route to ergod- icity and scarring in collective quantum systems, Journal of Physics: Condensed Matter36, 163001 (2024)

    2024

  6. [6]

    Kitagawa and M

    M. Kitagawa and M. Ueda, Squeezed spin states, Physical Review A47, 5138 (1993)

    1993

  7. [7]

    Ma and X

    J. Ma and X. Wang, Fisher information and spin squeez- ing in the lipkin-meshkov-glick model, Physical Review A80, 012318 (2009)

    2009

  8. [8]

    Jin, Y.-C

    G.-R. Jin, Y.-C. Liu, and W.-M. Liu, Spin squeezing in a generalized one-axis twisting model, New Journal of Physics11, 073049 (2009)

    2009

  9. [9]

    J. Ma, X. Wang, C.-P. Sun, and F. Nori, Quantum spin squeezing, Physics Reports509, 89 (2011)

    2011

  10. [10]

    Y. Liu, Z. Xu, G. Jin, and L. You, Spin squeezing: Trans- forming one-axis twisting into two-axis twisting, Physical review letters107, 013601 (2011)

    2011

  11. [11]

    M. H. Mu˜ noz-Arias, I. H. Deutsch, and P. M. Poggi, Phase-space geometry and optimal state preparation in quantum metrology with collective spins, PRX Quantum 4, 020314 (2023)

    2023

  12. [12]

    S. C. Carrasco, M. H. Goerz, S. A. Malinovskaya, V. Vuleti´ c, W. P. Schleich, and V. S. Malinovsky, Dicke state generation and extreme spin squeezing via rapid adiabatic passage, Physical Review Letters132, 153603 (2024)

    2024

  13. [13]

    Gangopadhay and S

    N. Gangopadhay and S. Choudhury, Counterdiabatic route to entanglement steering and dynamical freezing in the floquet lipkin-meshkov-glick model, Physical Re- view Letters135, 020407 (2025)

    2025

  14. [14]

    J. T. Reilly, S. B. J¨ ager, J. D. Wilson, J. Cooper, S. Eg- gert, and M. J. Holland, Speeding up squeezing with a pe- riodically driven dicke model, Physical Review Research 6, 033090 (2024)

    2024

  15. [15]

    Biswas and S

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

    work page arXiv 2025

  16. [16]

    Biswas and S

    H. Biswas and S. Choudhury, The floquet central spin model: A platform to realize eternal time crystals, entan- glement steering, and multiparameter metrology, arXiv preprint arXiv:2501.18472 (2025)

    work page arXiv 2025

  17. [17]

    Russomanno, F

    A. Russomanno, F. Iemini, M. Dalmonte, and R. Fazio, Floquet time crystal in the lipkin-meshkov-glick model, Physical Review B95, 214307 (2017)

    2017

  18. [18]

    Pizzi, J

    A. Pizzi, J. Knolle, and A. Nunnenkamp, Higher-order and fractional discrete time crystals in clean long-range interacting systems, Nature communications12, 2341 (2021)

    2021

  19. [19]

    C. Lyu, S. Choudhury, C. Lv, Y. Yan, and Q. Zhou, Eternal discrete time crystal beating the heisenberg limit, Physical Review Research2, 033070 (2020)

    2020

  20. [20]

    Lerose, T

    A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, Theory of robust quantum many-body scars in long-range interacting systems, Physical Review X15, 011020 (2025)

    2025

  21. [21]

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

    1954

  22. [22]

    B. M. Garraway, The dicke model in quantum optics: Dicke model revisited, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineer- ing Sciences369, 1137 (2011)

    2011

  23. [23]

    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)

    2019

  24. [24]

    M. M. Roses and E. G. Dalla Torre, Dicke model, PLoS One15, e0235197 (2020)

    2020

  25. [25]

    Frisk Kockum, A

    A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nature Reviews Physics1, 19 (2019)

    2019

  26. [26]

    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)

    1973

  27. [27]

    Y. K. Wang and F. T. Hioe, Phase transition in the dicke model of superradiance, Phys. Rev. A7, 831 (1973)

    1973

  28. [28]

    Emary and T

    C. Emary and T. Brandes, Quantum chaos triggered by precursors of a quantum phase transition: The dicke model, Phys. Rev. Lett.90, 044101 (2003)

    2003

  29. [29]

    Emary and T

    C. Emary and T. Brandes, Chaos and the quantum phase transition in the dicke model, Phys. Rev. E67, 066203 (2003)

    2003

  30. [30]

    R. J. Lewis-Swan, A. Safavi-Naini, J. J. Bollinger, and A. M. Rey, Unifying scrambling, thermalization and en- tanglement through measurement of fidelity out-of-time- order correlators in the dicke model, Nature communica- tions10, 1581 (2019)

    2019

  31. [31]

    Das and A

    P. Das and A. Sharma, Revisiting the phase transitions of the dicke model, Physical Review A105, 033716 (2022)

    2022

  32. [32]

    L. Song, D. Yan, J. Ma, and X. Wang, Spin squeezing as an indicator of quantum chaos in the dicke model, Physical Review E79, 046220 (2009)

    2009

  33. [33]

    M. A. Bastarrachea-Magnani, B. L´ opez-del Carpio, S. Lerma-Hern´ andez, and J. G. Hirsch, Chaos in the dicke model: quantum and semiclassical analysis, Phys- ica Scripta90, 068015 (2015)

    2015

  34. [34]

    L´ obez and A

    C. L´ obez and A. Rela˜ no, Entropy, chaos, and excited- state quantum phase transitions in the dicke model, Physical Review E94, 012140 (2016)

    2016

  35. [35]

    Comparative Study of Indicators of Chaos in the Closed and Open Dicke Model

    P. Pawar, A. Bhattacharyya, and B. P. Venkatesh, Comparative study of indicators of chaos in the closed and open dicke model, arXiv preprint arXiv:2505.10327 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  36. [36]

    Wang and M

    Q. Wang and M. Robnik, Statistical properties of the localization measure of chaotic eigenstates in the dicke model, Physical Review E102, 032212 (2020)

    2020

  37. [37]

    Baumann, C

    K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, nature464, 1301 (2010)

    2010

  38. [38]

    Klinder, H

    J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hem- merich, Dynamical phase transition in the open dicke model, Proceedings of the National Academy of Sciences 112, 3290 (2015)

    2015

  39. [39]

    M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, Realization of the dicke model using cavity-assisted raman transitions, Physical review letters 113, 020408 (2014)

    2014

  40. [40]

    J. A. Mlynek, A. A. Abdumalikov, C. Eichler, and A. Wallraff, Observation of dicke superradiance for two artificial atoms in a cavity with high decay rate, Nature communications5, 5186 (2014)

    2014

  41. [41]

    Tomonaga, R

    A. Tomonaga, R. Stassi, H. Mukai, F. Nori, F. Yoshi- hara, and J. Tsai, Spectral properties of two supercon- ducting artificial atoms coupled to a resonator in the ul- trastrong coupling regime, Nature communications16, 6 5294 (2025)

    2025

  42. [42]

    Safavi-Naini, R

    A. Safavi-Naini, R. J. Lewis-Swan, J. G. Bohnet, M. G¨ arttner, K. A. Gilmore, J. E. Jordan, J. Cohn, J. K. Freericks, A. M. Rey, and J. J. Bollinger, Verification of a many-ion simulator of the dicke model through slow quenches across a phase transition, Physical review let- ters121, 040503 (2018)

    2018

  43. [43]

    K. A. Gilmore, M. Affolter, R. J. Lewis-Swan, D. Barber- ena, E. Jordan, A. M. Rey, and J. J. Bollinger, Quantum- enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals, Science373, 673 (2021)

    2021

  44. [44]

    Bullock, S

    B. Bullock, S. R. Muleady, J. F. Lilieholm, Y. Zhang, A. Safavi-Naini, R. J. Lewis-Swan, J. J. Bollinger, A. M. Rey, and A. L. Carter, Quantum simulation of the dicke model in a two-dimensional ion crystal: chaos, quantum thermalization, and revivals, arXiv preprint arXiv:2602.06114 (2026)

    work page arXiv 2026

  45. [45]

    D. Kim, S. Dasgupta, X. Ma, J.-M. Park, H.-T. Wei, X. Li, L. Luo, J. Doumani, W. Yang, D. Cheng,et al., Observation of the magnonic dicke superradiant phase transition, Science advances11, eadt1691 (2025)

    2025

  46. [46]

    Baydin, H

    A. Baydin, H. Zhu, M. Bamba, K. R. Hazzard, and J. Kono, Perspective on the quantum vacuum in mat- ter, Optical Materials Express15, 1833 (2025)

    2025

  47. [47]

    Dimer, B

    F. Dimer, B. Estienne, A. Parkins, and H. Carmichael, Proposed realization of the dicke-model quantum phase transition in an optical cavity qed system, Physical Re- view A75, 013804 (2007)

    2007

  48. [48]

    E. I. R. Chiacchio, A. Nunnenkamp, and M. Brunelli, Nonreciprocal dicke model, Phys. Rev. Lett.131, 113602 (2023)

    2023

  49. [49]

    Keeling, M

    J. Keeling, M. Bhaseen, and B. Simons, Collective dy- namics of bose-einstein condensates in optical cavities, Physical review letters105, 043001 (2010)

    2010

  50. [50]

    M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, Dynamics of nonequilibrium dicke models, Phys. Rev. A 85, 013817 (2012)

    2012

  51. [51]

    K. C. Stitely, A. Giraldo, B. Krauskopf, and S. Parkins, Nonlinear semiclassical dynamics of the unbalanced, open dicke model, Phys. Rev. Res.2, 033131 (2020)

    2020

  52. [52]

    Mivehvar, Conventional and unconventional dicke models: Multistabilities and nonequilibrium dynamics, Phys

    F. Mivehvar, Conventional and unconventional dicke models: Multistabilities and nonequilibrium dynamics, Phys. Rev. Lett.132, 073602 (2024)

    2024

  53. [53]

    Alavirad and A

    Y. Alavirad and A. Lavasani, Scrambling in the dicke model, Physical Review A99, 043602 (2019)

    2019

  54. [54]

    Buijsman, V

    W. Buijsman, V. Gritsev, and R. Sprik, Nonergodicity in the anisotropic dicke model, Physical Review Letters 118, 080601 (2017)

    2017

  55. [55]

    P. Das, D. S. Bhakuni, and A. Sharma, Phase transitions of the anisotropic dicke model, Physical Review A107, 043706 (2023)

    2023

  56. [56]

    Zhu, J.-H

    X. Zhu, J.-H. L¨ u, W. Ning, L.-T. Shen, F. Wu, and Z.-B. Yang, Quantum geometric tensor and critical metrology in the anisotropic dicke model, Physical Review A109, 052621 (2024)

    2024

  57. [57]

    superradiant

    A. Baksic and C. Ciuti, Controlling discrete and continu- ous symmetries in “superradiant” phase transitions with circuit qed systems, Physical Review Letters112, 173601 (2014)

    2014

  58. [58]

    Soriente, T

    M. Soriente, T. Donner, R. Chitra, and O. Zilberberg, Dissipation-induced anomalous multicritical phenomena, Physical review letters120, 183603 (2018)

    2018

  59. [59]

    Mahmoodian, Chiral light-matter interaction beyond the rotating-wave approximation, Phys

    S. Mahmoodian, Chiral light-matter interaction beyond the rotating-wave approximation, Phys. Rev. Lett.123, 133603 (2019)

    2019

  60. [60]

    J. Fan, Z. Yang, Y. Zhang, J. Ma, G. Chen, and S. Jia, Hidden continuous symmetry and nambu-goldstone mode in a two-mode dicke model, Phys. Rev. A89, 023812 (2014)

    2014

  61. [61]

    N. N. Bogolubov and N. N. Bogolubov Jr, Introduction to Quantum Statistical Mechan- ics, 2nd ed. (WORLD SCIENTIFIC, 2009) https://www.worldscientific.com/doi/pdf/10.1142/7623

    work page doi:10.1142/7623 2009

  62. [62]

    See Supplemental Material for the detailed derivation of the main results

  63. [63]

    Prakash, M

    A. Prakash, M. Fava, and S. A. Parameswaran, Multiver- sality and unnecessary criticality in one dimension, Phys. Rev. Lett.130, 256401 (2023)

    2023

  64. [64]

    Damanet, A

    F. Damanet, A. J. Daley, and J. Keeling, Atom-only de- scriptions of the driven-dissipative dicke model, Physical Review A99, 033845 (2019)

    2019

  65. [65]

    M¨ uller and W

    K. M¨ uller and W. T. Strunz, Genuine quantum effects in dicke-type models at large atom numbers, Physical Review Letters135, 123602 (2025)

    2025

  66. [66]

    Mondal, L

    D. Mondal, L. F. Santos, and S. Sinha, Transient and steady-state chaos in dissipative quantum systems, Phys- ical Review Letters136, 040401 (2026)

    2026

  67. [67]

    Z. Gong, R. Hamazaki, and M. Ueda, Discrete time- crystalline order in cavity and circuit qed systems, Phys- ical review letters120, 040404 (2018)

    2018

  68. [68]

    B. Zhu, J. Marino, N. Y. Yao, M. D. Lukin, and E. A. Demler, Dicke time crystals in driven-dissipative quan- tum many-body systems, New Journal of Physics21, 073028 (2019)

    2019

  69. [69]

    B. Das, N. Jaseem, and V. Mukherjee, Discrete time crys- tals in the presence of non-markovian dynamics, Physical Review A110, 012208 (2024)

    2024

  70. [70]

    S. B. J¨ ager, J. M. Giesen, I. Schneider, and S. Eggert, Dissipative dicke time crystals: An atom’s point of view, Physical Review A110, L010202 (2024)

    2024

  71. [71]

    J. G. Cosme, J. Skulte, and L. Mathey, Bridging closed and dissipative discrete time crystals in spin systems with infinite-range interactions, Physical Review B108, 024302 (2023)

    2023

  72. [72]

    P. Das, D. S. Bhakuni, L. F. Santos, and A. Sharma, Pe- riodically and quasiperiodically driven anisotropic dicke model, Physical Review A108, 063716 (2023)

    2023

  73. [73]

    Anisur and S

    S. Anisur and S. Choudhury, Dissipative dicke time qua- sicrystals, arXiv preprint arXiv:2602.05994 (2026)

    work page arXiv 2026

  74. [75]

    J. Rohn, M. H¨ ormann, C. Genes, and K. P. Schmidt, Ising model in a light-induced quantized transverse field, Phys. Rev. Res.2, 023131 (2020)

    2020

  75. [76]

    Langheld, M

    A. Langheld, M. H¨ ormann, and K. P. Schmidt, Quan- tum phase diagrams of dicke-ising models by a wormhole algorithm, Phys. Rev. B112, L161123 (2025)

    2025

  76. [77]

    Z. Li, S. Choudhury, and W. V. Liu, Fast scrambling without appealing to holographic duality, Physical Re- view Research2, 043399 (2020)

    2020

  77. [78]

    Z. Li, S. Choudhury, and W. V. Liu, Long-range-ordered phase in a quantum heisenberg chain with interac- tions beyond nearest neighbors, Physical Review A104, 013303 (2021)

    2021

  78. [79]

    (2N−3|α 3|2) 2 p N− |α 3|2 − U|α3|2p N− |α 3|2 ˜ωc +U|α 3|2 # (˜a† 1˜a3 + ˜a† 3˜a1) − g1√ N

    J. Rom´ an-Roche,´A. G´ omez-Le´ on, F. Luis, and D. Zueco, 7 Bound polariton states in the dicke–ising model, Nanophotonics14, 2053 (2025). 1 Supplemental Material: Robust continuous symmetry breaking and multiversality in the chiral Dicke model Nikolay Yegovtsev,1 Sayan Choudhury,2,3 W. Vincent Liu1 1Department of Physics and Astronomy and IQ Initiative...

    2053

  79. [80]

    We note that in theU→0 regime, we substitute ˜ωc →ω c, and|α 3|2 = N 2 1− ωzωc g2 1+g2 2

    respectively. We note that in theU→0 regime, we substitute ˜ωc →ω c, and|α 3|2 = N 2 1− ωzωc g2 1+g2 2 . Diagonalization procedure forU= 0 We now outline the procedure to diagonalize the Bogoliubov Hamiltonian whenU= 0. In this case, the most general quadratic Hamiltonian can be written in the form: HB = 3X i=1 3X j=1 Aij˜a† i ˜aj + 1 2 Bij˜a† i ˜a† j + 1...

  80. [81]

    + (g2 1 −ω zωc)2,(S.11) leading to the following solutions: ε±(g1) = s ω2z +ω 2c + 2g2 1 ± p (ω2z −ω 2c)2 + 4g2 1(ωz +ω c)2 2 .(S.12) When we approach the critical couplingg c, we can expand theε − aroundg c = √ωzωc to obtain: ε− = 2√ωzωc (ωz +ω c) |gc −g 1|.(S.13) We can extract how the gap closes as we approach the critical pointg c = √ωzωc from the nor...

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