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A hybrid variational solver can match converged spin-boson DMRG accuracy in the Dicke and Dicke-Ising models while operating at a substantially reduced tensor-network bond dimension.

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2026-08-01 16:34 UTC pith:ZTKT7IOY

load-bearing objection A solid, reproducible methods paper that validates NGS+DMRG on collective single-mode Dicke models; the broader multi-mode/spin-Holstein claim is explicit future work, not demonstrated. the 2 major comments →

arxiv 2607.17934 v1 pith:ZTKT7IOY submitted 2026-07-20 quant-ph

Variational non-gaussian approach to interacting spin-boson models

Jo\~ao Pedro Mendon\c{c}a , Yao Wang , Krzysztof Jachymski This is my paper
classification quant-ph
keywords spin-boson modelsDicke modelDicke-Ising modelnon-Gaussian variational statesdressing transformationDMRGcavity QEDsuperradiant phase transition
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that strongly correlated spin-boson problems can be solved without truncating the bosonic Hilbert space by folding the boson mode and spin-boson entanglement into a compact non-Gaussian variational state, then solving only an effective spin Hamiltonian with DMRG. The central claim is that this hybrid loop is both accurate and cheaper: on the Dicke and Dicke-Ising models it reproduces converged spin-boson DMRG ground-state energies, order parameters, and phase boundaries with substantially reduced MPS bond dimension and runtime. If true, it offers a practical route to cavity-QED, spin-phonon, and related models where bosonic occupation is large and spin correlations are strong, without perturbatively eliminating the bosons. The key object is a variational dressing transformation that promotes the canonical polaron frame change into a tunable parameter, thereby generating photon-mediated all-to-all spin interactions that DMRG can handle.

Core claim

The paper claims that the ground state of a spin-boson Hamiltonian can be well approximated by writing it as |ψ_NGS⟩ = U_λ U_GS |0_b⟩ ⊗ |φ_s⟩, where U_GS is a Gaussian displacement-and-squeezing operation and U_λ = exp(i g'/ω λ S_x p) is a variational spin-dependent displacement. Holding the bosonic variational parameters fixed, the dressed problem reduces to an effective spin Hamiltonian with photon-mediated all-to-all (S_x)^2 interactions, whose ground state φ_s is computed by DMRG; the loop is iterated to self-consistency. Benchmarked on the Dicke and Dicke-Ising models from N=10 to 100, the resulting energies, photon numbers, magnetizations, staggered magnetization, and phase boundaries—

What carries the argument

The load-bearing object is the non-Gaussian variational ansatz and its dressing transformation. U_λ = exp(i g'/ω λ S_x p) promotes the canonical polaron frame change from a fixed transformation to a variational layer controlled by λ: λ=0 gives a separable Gaussian state, while λ=1 corresponds to the polaron-decoupled frame. Applying U_λ to the Dicke Hamiltonian turns the linear spin-photon coupling into a photon-mediated all-to-all spin interaction ∼(S_x)^2 plus renormalized fields and squeezing-dependent exponentials, so that after averaging over the bosonic Gaussian layer the problem becomes an effective spin Hamiltonian. DMRG solves that spin problem, and the variational parameters (dress

Load-bearing premise

The ansatz is restricted to a homogeneous single-mode dressing G1 = λ S_x p plus diagonal squeezing (Sec. IV A 2; Appendix D), and its accuracy is benchmarked only on single-mode Dicke-type models; if real ground states require site-dependent dresses, multiple modes, or non-Gaussian bosonic fluctuations beyond squeezing in the targeted regimes, the claimed accuracy is not established.

What would settle it

Run the same NGS-DMRG loop on a spin-Holstein chain with local phonon modes and site-resolved couplings, which the paper's general formalism permits but does not test, and compare against converged multi-mode DMRG for N=8–16: if the energy error does not decay with N, or the bond-dimension advantage disappears, the single-mode homogeneous manifold is missing correlations the method claims to capture.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • For the Dicke and Dicke-Ising models at N=10–100, the method reproduces converged spin-boson DMRG energies and order parameters while needing much smaller MPS bond dimensions, with the largest savings near the phase transition and in the AFM-superradiant coexistence window.
  • Because no photon cutoff is introduced on the variational side, the approach is designed for strong-coupling regimes where converged reference DMRG needs large photon truncation (up to n_max=350 for N=100 in the benchmarks).
  • The nested-manifold hierarchy implies that adding higher-order dressing generators (e.g., S_y x terms) yields a strictly lower variational energy, providing an in-principle systematic route toward controlled accuracy.
  • The framework is set up for multi-mode, site-dependent, and inhomogeneous couplings (e.g., spin-Holstein models), so the same solver architecture can be carried beyond the single-mode cavity limit.

Where Pith is reading between the lines

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

  • The single-mode homogeneous manifold is likely to underestimate correlations in models with local phonon modes or multiple cavities; a natural test is to allow site-dependent λ_im in the general dressing and compare against exact small-system results.
  • The optimized λ itself can be read as a quantitative measure of spin-boson entanglement: monitoring its finite-size flow could locate where the semi-classical λ→0 or polaron λ→1 limits become exact.
  • The runtime advantage may be specific to low-dimensional spin geometries, since the effective Hamiltonian carries a long-range (S_x)^2 term that becomes expensive for 2D and 3D backends; the paper's proposed extension to PEPS or neural quantum states would test this.
  • The claim that the thermodynamic limit of the Dicke-Ising model has vanishing spin-photon entanglement could be sharpened by computing the dressed correlator ⟨(S_x)^2⟩_NGS as a function of N and extracting its finite-size scaling exponent.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper introduces a hybrid variational method for interacting spin-boson Hamiltonians. The bosonic sector is represented by a Gaussian state with displacement and squeezing, augmented by a variational spin-dependent displacement (dressing) transformation that captures spin-boson correlations. Tracing out the bosons leads to an effective spin Hamiltonian that is solved by DMRG, and the variational parameters are optimized in a self-consistent loop. The general formalism is derived for multi-mode, site-dependent couplings, but the numerical implementation is specialized to homogeneous single-mode cavity-QED models. The method is benchmarked on the Dicke and Dicke-Ising models against converged spin-boson DMRG with explicit photon truncation. The authors report accurate ground-state energies and order parameters, lower MPS bond dimensions, and reduced runtime compared with the reference solver, with energy errors decreasing with system size.

Significance. If the claims hold, the proposed NGS-DMRG scheme is a useful alternative to explicit bosonic truncation in spin-boson DMRG, particularly for strongly coupled cavity-QED systems where the bosonic Hilbert space is large. The paper has clear strengths: explicit algebraic derivations of the effective spin Hamiltonian, a self-consistent variational loop, benchmarks against a well-converged external solver, checks of the photon-number cutoff in the reference calculations, and a publicly available code and data set. The manuscript also proposes a systematic manifold hierarchy for future accuracy improvements. The main gap is that the numerical validation is restricted to homogeneous single-mode collective models, whereas the general target class stated in Eq. (1) includes site-dependent and multi-mode couplings; this limits the scope of the broader claims.

major comments (2)
  1. [Sec. III B, Eq. (14); Sec. VI; Figs. 2–5] The paper's stated target is the general Hamiltonian in Eq. (1), and Appendix B derives an effective Hamiltonian for the multi-mode, site-dependent dressing of Eq. (14). However, every numerical benchmark (Dicke and Dicke-Ising models, Figs. 2–5 and Appendices E–F) uses the homogeneous single-mode collective form. The text itself acknowledges this at Sec. III B ('we focus on the homogeneous single-mode form relevant to the cavity-QED limit') and Sec. VI ('our next step is to expand the software to include these models'). As a result, the broad claims about an 'interacting spin-boson' framework are validated only for a restricted subclass. I recommend either adding at least one proof-of-principle calculation for a site-dependent or multi-mode case (e.g., a spin-Holstein model, Eq. (5)), or explicitly restricting the title, abstract, and conclusions to 'single-mode cavity-QED models' and s
  2. [Sec. V, Fig. 4; Appendix F] The accuracy claim is based on the absolute energy error |E0 − E_ref0| relative to reference DMRG. This quantity is not normalized by N or by the relevant energy scale, so the reported errors are difficult to interpret across system sizes. Additionally, the main text (Fig. 4b) states that the error decays 'algebraically' with N, while Appendix F says it decays 'roughly exponentially' with N. These statements are inconsistent and should be reconciled. The reference-DMRG photon-cutoff convergence check in Appendix E is shown only for N = 40, J = 0.8, while the benchmark uses nmax up to 350 for N = 100; a concise convergence summary for the largest system sizes and other J values would substantiate that the reference calculations are truly converged.
minor comments (5)
  1. [Fig. 2 caption and text] The caption lists only panels (a) and (b), but the text refers to 'Fig. 2(c)' for order parameters and to 'Fig. 2(b)' for non-Gaussian energies. The panel labels and caption should be corrected to match the actual figure.
  2. [Eq. (2)] The notation 'g′Sxx' is ambiguous; it should read g′ S_x x (or equivalent) to distinguish the spin operator S_x from the photon quadrature x.
  3. [Sec. IV A 2] The restriction of the covariance matrix to diagonal form, Γ = diag{e^{2ξ}/2, e^{−2ξ}/2}, assumes no x–p correlations. This is a variational restriction that is not justified in the text. A sentence explaining why this is expected to be optimal for Dicke-type coupling (or noting it as an additional ansatz constraint) would strengthen the presentation.
  4. [Sec. V, Fig. 5(b)] The convergence plot shows the energy difference per iteration, but the stopping criterion for the self-consistent outer loop is not stated in the main text or caption. The authors should specify the tolerance used.
  5. [Figs. 2, 4, 5] The photon cutoffs nmax are listed with different values for the same N in different figures (e.g., N = 10 appears as 40 in Fig. 2 and 30 in Figs. 4–5). The notation should be unified or explained.

Circularity Check

0 steps flagged

No significant circularity: NGS-DMRG is a variational method externally benchmarked against converged spin-boson DMRG.

full rationale

The derivation chain is self-contained. The non-Gaussian state is a variational family; the parameters {ΔR, Γ, λ} are fixed by minimizing ⟨H⟩_NGS, not by fitting to the reference data (Sec. III C, Eqs. 15-17, 22-23; Appendix B). The effective spin Hamiltonian is obtained by exact unitary dressing and Gaussian averaging, and the spin state is the DMRG ground state of that effective Hamiltonian; this is a self-consistent solution of the same Hamiltonian, not an input-equal-output construction. The benchmark against reference DMRG is external: the reference solver explicitly truncates the photon Hilbert space at a converged n_max with a stated convergence criterion (Sec. IV; Appendix E), and the NGS results are not fed into it. The inequalities E_GS ≥ E_NGS ≥ E0 follow from manifold nesting M_GS ⊆ M_NGS and the variational principle, so they are consequences, not assumptions. The same-author citations (Ref. 48; Refs. 84-85 include a co-author) motivate the homogeneous single-mode restriction and the leading-order G_1 truncation, but the central accuracy claims are independently validated in this paper by comparison to converged spin-boson DMRG (Figs. 2-5, Appendices E-F). The restrictions to λS_x p dressing and single-mode homogeneous couplings are explicitly identified as scope limitations with multi-mode/site-dependent models deferred to future work (Sec. III B; Sec. VI; Appendix D); this is a coverage caveat, not a circular reduction. No equation in the paper reduces to a fitted parameter renamed as a prediction, and no load-bearing uniqueness theorem is imported from the authors' prior work.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

No empirical constants are fitted to the target data. The only free inputs are the variational ansatz parameters λ and ξ, which are energy-minimized. The central non-trivial input is the ansatz manifold itself; accuracy is benchmarked externally against converged reference DMRG, so the empirical support is independent of the authors' earlier results.

free parameters (2)
  • Dressing amplitude λ = variational, optimized per (g,J,N)
    Controls spin-boson correlations in U_λ = exp(i g' S_x p / ω). Minimized in the self-consistent loop, not fitted to reference data, but a degree of freedom of the ansatz.
  • Squeezing parameter ξ = variational, optimized per (g,J,N)
    Diagonal covariance Γ = diag(e^{2ξ}/2, e^{-2ξ}/2). Minimized in the energy loop, not fitted to target data.
axioms (5)
  • standard math Wick's theorem exactly evaluates expectation values in Gaussian states.
    Used in Sec. III A and Appendix C to compute variational energy and observables on U_GS|0>.
  • standard math Variational principle: minimized energy over a nested manifold gives upper bounds E_GS ≥ E_NGS ≥ E0.
    Sec. III C uses this to justify improvement of NGS over GS; follows from minimization over a larger set.
  • domain assumption The homogeneous single-mode manifold (collective λ S_x dressing, diagonal covariance) is expressive enough for Dicke and Dicke-Ising ground states.
    Imposed in Sec. IV A 2; supported by benchmarks for tested N, g, J, but not established for general spin-boson models.
  • domain assumption DMRG returns accurate ground states of the effective spin Hamiltonian at each self-consistent iteration.
    Numerical backend used throughout; convergence tolerances stated in Sec. V and footnote [105].
  • domain assumption Reference spin-boson DMRG with finite, converged n_max is a reliable exact benchmark.
    Convergence checked by increasing n_max (Appendix E, Fig. 6), but any finite truncation is an approximation.

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read the original abstract

We apply a hybrid variational framework to interacting spin-boson Hamiltonians, targeting regimes where simulations are limited by the unbounded bosonic Hilbert space and strong many-body correlations. The bosonic sector and spin-boson correlations are captured within a compact non-Gaussian variational manifold, while the minimized spin sector is obtained as the solution to an effective spin Hamiltonian. Minimization is carried out inside a self-consistent energy-minimization loop, where variational parameters are minimized and the effective Hamiltonian is solved via DMRG. The results are obtained without eliminating or truncating the photonic field. We benchmark the method on the Dicke and Dicke-Ising models by comparison to converged spin-boson DMRG, finding accurate ground-state solutions with reduced bond dimension.

Figures

Figures reproduced from arXiv: 2607.17934 by Jo\~ao Pedro Mendon\c{c}a, Krzysztof Jachymski, Yao Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. Self-consistent optimization loop. For fixed bosonic [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Dicke model observables for the three solvers and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dicke-Ising model phase diagram and observables. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Computational cost comparison for the Dicke-Ising [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Maximum bond dimension of both NGS-DMRG and [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Convergence of the boson truncation for reference [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Energy error of the NGS-DMRG method with re [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗

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Reference graph

Works this paper leans on

115 extracted references · 1 canonical work pages

  1. [1]

    mean-field

    Gaussian solution As a baseline, we first consider the separable Gaussian limit in which the bosonic mode is described by a dis- placed vacuum. In practice, this corresponds to a cav- ity mean-field treatment where the bosonic operator is replaced by a c-number,a→ ⟨a⟩ ≡αor equivalently x→ ⟨x⟩ ≡∆x, and we set⟨p⟩= 0 as it minimizes to zero. The resulting ef...

  2. [2]

    Because the coupling is uniform, we rep- resent the dressing transformation as a collective spin rotation about thexaxis,λ α j1 =λ(g ′/ω)δαx

    NGS Solutions Applying the NGS framework to the homogeneous single-mode Dicke interaction allows us to first simplify the non-Gaussian manifold using physically motivated constraints. Because the coupling is uniform, we rep- resent the dressing transformation as a collective spin rotation about thexaxis,λ α j1 =λ(g ′/ω)δαx. In the bosonic sector, the rest...

  3. [3]

    FM regime We start in the ferromagnetic regimeJ > Jc, where the Ising coupling favors spin alignment alongz. For mod- erate values ofJ≲0.5, the normal state remains adia- batically connected to the Dicke normal phase and the main effect of the Ising coupling is the renormalization of the atomic excitation gap as explained below. This provides a simple ana...

  4. [4]

    In this regime, a direct continuous connec- tion between antiferromagnetic-normal (AFM-NP) and paramagnetic-superradiant phases (PM-SP) is not ex- pected within Landau theory

    AFM regime We now turn to the antiferromagnetic caseJ < J c, where the competition between antiferromagnetic Ising interactions (J <0) and the longitudinal fieldεfavors an AFM-ordered state at smallg, with a vanishing pho- ton number. In this regime, a direct continuous connec- tion between antiferromagnetic-normal (AFM-NP) and paramagnetic-superradiant p...

  5. [5]

    Quan- tum Optical Technologies

    Summary In summary, we applied the NGS-DMRG numerical framework to characterize the phases of the well-known Dicke-Ising model. We observed the entire variety of phases and QPTs reported in recent works. NGS-DMRG overlaps well with reference DMRG forN= 100, show- ing that our method is capable of reproducing results of established numerical methods. Addit...

    2023

  6. [6]

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissi- pative two-state system, Rev. Mod. Phys.59, 1 (1987)

    1987

  7. [7]

    Schlawin, D

    F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Applied Physics Reviews9, 011312 (2022)

    2022

  8. [8]

    Basov, A

    D. Basov, A. Asenjo-Garcia, P. J. Schuck, X. Zhu, A. Rubio, A. Cavalleri, M. Delor, M. M. Fogler, and M. Liu, Polaritonic quantum matter, Nanophotonics doi:10.1515/nanoph-2025-0001 (2025)

    doi:10.1515/nanoph-2025-0001 2025

  9. [9]

    I. I. Rabi, On the process of space quantization, Phys. Rev.49, 324 (1936)

    1936

  10. [10]

    Jaynes and F

    E. Jaynes and F. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proceedings of the IEEE51, 89 (1963)

    1963

  11. [11]

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

    1954

  12. [12]

    Forn-D ´ ıaz, L

    P. Forn-D ´ ıaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Ultrastrong coupling regimes of light-matter interaction, Rev. Mod. Phys.91, 025005 (2019)

    2019

  13. [13]

    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

  14. [14]

    Blais, R.-S

    A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A69, 062320 (2004)

    2004

  15. [15]

    R. J. Schoelkopf and S. M. Girvin, Wiring up quantum systems, Nature451, 664 (2008)

    2008

  16. [16]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys.93, 025005 (2021)

    2021

  17. [17]

    M. C. Cross and D. S. Fisher, A new theory of the spin- peierls transition with special relevance to the experi- ments on ttfcubdt, Phys. Rev. B19, 402 (1979)

    1979

  18. [18]

    M. Hase, I. Terasaki, and K. Uchinokura, Observation of the spin-peierls transition in linear cu 2+ (spin-1/2) chains in an inorganic compound cugeo 3, Phys. Rev. Lett.70, 3651 (1993)

    1993

  19. [19]

    Kiryukhin, B

    V. Kiryukhin, B. Keimer, and D. E. Moncton, Direct observation of a magnetic field induced commensurate- incommensurate transition in a spin-peierls system, Phys. Rev. Lett.74, 1669 (1995)

    1995

  20. [20]

    D. H. Moseley, S. E. Stavretis, K. Thirunavukkuarasu, M. Ozerov, Y. Cheng, L. L. Daemen, J. Ludwig, Z. Lu, D. Smirnov, C. M. Brown,et al., Spin–phonon couplings in transition metal complexes with slow magnetic relax- ation, Nature Communications9, 2572 (2018)

    2018

  21. [21]

    S. D. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, and M. D. Lukin, Phonon-induced spin-spin interactions in diamond nanostructures: Application to spin squeezing, Phys. Rev. Lett.110, 156402 (2013)

    2013

  22. [22]

    P.-B. Li, Y. Zhou, W.-B. Gao, and F. Nori, Enhancing spin-phonon and spin-spin interactions using linear re- sources in a hybrid quantum system, Phys. Rev. Lett. 125, 153602 (2020)

    2020

  23. [23]

    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, Ver- ification of a many-ion simulator of the dicke model through slow quenches across a phase transition, Phys. Rev. Lett.121, 040503 (2018)

    2018

  24. [24]

    Marquez Peraca, X

    N. Marquez Peraca, X. Li, J. M. Moya, K. Hayashida, D. Kim, X. Ma, K. J. Neubauer, D. Fallas Padilla, C.-L. Huang, P. Dai, A. H. Nevidomskyy, H. Pu, E. Morosan, S. Cao, M. Bamba, and J. Kono, Quantum simulation of an extended dicke model with a magnetic solid, Com- munications Materials5, 42 (2024)

    2024

  25. [25]

    Colombo, E

    S. Colombo, E. Pedrozo-Pe˜ nafiel, A. F. Adiyatullin, Z. Li, E. Mendez, C. Shu, and V. Vuleti´ c, Time-reversal- based quantum metrology with many-body entangled states, Nature Physics18, 925 (2022)

    2022

  26. [26]

    Franke, S

    J. Franke, S. R. Muleady, R. Kaubruegger, F. Kranzl, R. Blatt, A. M. Rey, M. K. Joshi, and C. F. Roos, Quantum-enhanced sensing on optical transi- tions through finite-range interactions, Nature621, 740 (2023)

    2023

  27. [27]

    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

  28. [28]

    Campaioli, S

    F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: quantum batteries, Reviews of Modern Physics96, 031001 (2024)

    2024

  29. [29]

    J. Q. Quach, K. E. McGhee, L. Ganzer, D. M. Rouse, B. W. Lovett, E. M. Gauger, J. Keeling, G. Cerullo, D. G. Lidzey, and T. Virgili, Superabsorption in an or- ganic microcavity: Toward a quantum battery, Science advances8, eabk3160 (2022)

    2022

  30. [30]

    Otterpohl, D

    F. Otterpohl, D. Keefer, S. Mukamel, and M. Thorwart, Coherent ultrafast stimulated x-ray raman spectroscopy of dissipative conical intersections, Physical Review Let- ters133, 098001 (2024)

    2024

  31. [31]

    Porras and J

    D. Porras and J. I. Cirac, Effective quantum spin sys- tems with trapped ions, Phys. Rev. Lett.92, 207901 (2004)

    2004

  32. [32]

    S. F. Caballero-Benitez and I. B. Mekhov, Quantum optical lattices for emergent many-body phases of ul- tracold atoms, Phys. Rev. Lett.115, 243604 (2015)

    2015

  33. [33]

    Rom´ an-Roche and D

    J. Rom´ an-Roche and D. Zueco, Effective theory for mat- ter in non-perturbative cavity QED, SciPost Phys. Lect. Notes , 50 (2022). 13

    2022

  34. [34]

    Granet, Exact mean-field solution of a spin chain with short-range and long-range interactions, SciPost Phys.14, 133 (2023)

    E. Granet, Exact mean-field solution of a spin chain with short-range and long-range interactions, SciPost Phys.14, 133 (2023)

    2023

  35. [35]

    Majer, J

    J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Coupling superconduct- ing qubits via a cavity bus, Nature449, 443 (2007)

    2007

  36. [36]

    Kim, M.-S

    K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, Entanglement and tunable spin- spin couplings between trapped ions using multiple transverse modes, Phys. Rev. Lett.103, 120502 (2009)

    2009

  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]

    Ritsch, P

    H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical po- tentials, Rev. Mod. Phys.85, 553 (2013)

    2013

  39. [39]

    Landig, L

    R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Quantum phases from competing short-and long-range interactions in an opti- cal lattice, Nature532, 476 (2016)

    2016

  40. [40]

    Periwal, E

    A. Periwal, E. S. Cooper, P. Kunkel, J. F. Wienand, E. J. Davis, and M. Schleier-Smith, Programmable in- teractions and emergent geometry in an array of atom clouds, Nature600, 630 (2021)

    2021

  41. [41]

    A. V. Bezvershenko, C.-M. Halati, A. Sheikhan, C. Kol- lath, and A. Rosch, Dicke transition in open many-body systems determined by fluctuation effects, Phys. Rev. Lett.127, 173606 (2021)

    2021

  42. [42]

    Otterpohl, P

    F. Otterpohl, P. Nalbach, and M. Thorwart, Hidden phase of the spin-boson model, Phys. Rev. Lett.129, 120406 (2022)

    2022

  43. [43]

    G. Orso, J. Zakrzewski, and P. Deuar, Self-organized cavity bosons beyond the adiabatic elimination approx- imation, Phys. Rev. Lett.134, 183405 (2025)

    2025

  44. [44]

    Tolle, A

    L. Tolle, A. Sheikhan, T. Giamarchi, C. Kollath, and C.- M. Halati, Fluctuation-induced bistability of fermionic atoms coupled to a dissipative cavity, Phys. Rev. Lett. 134, 133602 (2025)

    2025

  45. [45]

    M. L. Wall, A. Safavi-Naini, and A. M. Rey, Simulating generic spin-boson models with matrix product states, Phys. Rev. A94, 053637 (2016)

    2016

  46. [46]

    D. S. Shapiro, Y. Weber, T. Bode, F. K. Wilhelm, and D. Bagrets, Digital-analog simulations of schr¨ odinger cat states in the dicke-ising model, Phys. Rev. A112, 042412 (2025)

    2025

  47. [47]

    Lepp¨ akangas, J

    J. Lepp¨ akangas, J. Braum¨ uller, M. Hauck, J.-M. Reiner, I. Schwenk, S. Zanker, L. Fritz, A. V. Ustinov, M. Wei- des, and M. Marthaler, Quantum simulation of the spin- boson model with a microwave circuit, Phys. Rev. A97, 052321 (2018)

    2018

  48. [48]

    Weber, Quantum monte carlo simulation of spin- boson models using wormhole updates, Phys

    M. Weber, Quantum monte carlo simulation of spin- boson models using wormhole updates, Phys. Rev. B 105, 165129 (2022)

    2022

  49. [49]

    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

  50. [50]

    B.-Y. Dong, Y. Liang, S. Chesi, and X.-F. Zhang, Quantum phase transitions of the anisotropic dicke-ising model in driven rydberg arrays (2025), arXiv:2511.22230 [cond-mat.quant-gas]

    arXiv 2025

  51. [51]

    Kn¨ orzer, T

    J. Kn¨ orzer, T. Shi, E. Demler, and J. I. Cirac, Spin- holstein models in trapped-ion systems, Phys. Rev. Lett. 128, 120404 (2022)

    2022

  52. [52]

    Garwo la and D

    J. Garwo la and D. Segal, Compact cavity-dressed hamil- tonian framework at arbitrarily strong light-matter cou- pling (2025), arXiv:2511.11903 [quant-ph]

    Pith/arXiv arXiv 2025

  53. [53]

    J. P. Mendon¸ ca, K. Jachymski, and Y. Wang, Role of matter interactions in superradiant phenomena, Phys. Rev. Lett.135, 133601 (2025)

    2025

  54. [54]

    Zhang, E

    C. Zhang, E. Jeckelmann, and S. R. White, Density matrix approach to local hilbert space reduction, Phys. Rev. Lett.80, 2661 (1998)

    1998

  55. [55]

    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

  56. [56]

    Gammelmark and K

    S. Gammelmark and K. Mølmer, Phase transitions and heisenberg limited metrology in an ising chain inter- acting with a single-mode cavity field, New Journal of Physics13, 053035 (2011)

    2011

  57. [57]

    Schellenberger and K

    A. Schellenberger and K. P. Schmidt, To infinity and back – 1/ngraph expansions of light-matter systems (2026), arXiv:2601.13860 [cond-mat.str-el]

    arXiv 2026

  58. [58]

    Leibig, M

    J. Leibig, M. H¨ ormann, A. Langheld, A. Schellen- berger, and K. P. Schmidt, Quantitative approach for the dicke-ising chain with an effective self-consistent matter hamiltonian (2026), arXiv:2601.10210 [quant- ph]

    arXiv 2026

  59. [59]

    J. A. Koziol, Quantum criticality of the ferromag- netic dicke-ising model (2026), arXiv:2605.27484 [ond- mat.str-el]

    Pith/arXiv arXiv 2026

  60. [60]

    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, Ad- vanced Quantum Technologies2, 1800043 (2019)

    2019

  61. [61]

    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

  62. [62]

    Hepp and E

    K. Hepp and E. H. Lieb, On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model, Annals of Physics76, 360 (1973)

    1973

  63. [63]

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

    1973

  64. [64]

    Rza˙ zewski, K

    K. Rza˙ zewski, K. W´ odkiewicz, and W.˙Zakowicz, Phase transitions, two-level atoms, and theA 2 term, Phys. Rev. Lett.35, 432 (1975)

    1975

  65. [65]

    Bialynicki-Birula and K

    I. Bialynicki-Birula and K. Rza ¸ ˙ zewski, No-go theorem concerning the superradiant phase transition in atomic systems, Phys. Rev. A19, 301 (1979)

    1979

  66. [66]

    Gaw¸ edzki and K

    K. Gaw¸ edzki and K. Rza ¸ ´ zewski, No-go theorem for the superradiant phase transition without dipole approxi- mation, Phys. Rev. A23, 2134 (1981)

    1981

  67. [67]

    Dimer, B

    F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, Proposed realization of the dicke-model quantum phase transition in an optical cavity qed sys- tem, Phys. Rev. A75, 013804 (2007)

    2007

  68. [68]

    Nataf and C

    P. Nataf and C. Ciuti, No-go theorem for superradiant quantum phase transitions in cavity qed and counter- example in circuit qed, Nature Communications1, 72 (2010)

    2010

  69. [69]

    D. Kim, S. Dasgupta, X. Ma, J.-M. Park, H.-T. Wei, X. Li, L. Luo, J. Doumani, W. Yang, D. Cheng, R. H. J. Kim, H. O. Everitt, S. Kimura, H. Nojiri, J. Wang, 14 S. Cao, M. Bamba, K. R. A. Hazzard, and J. Kono, Observation of the magnonic dicke superradiant phase transition, Science Advances11, eadt1691 (2025)

    2025

  70. [70]

    Vukics and P

    A. Vukics and P. Domokos, Adequacy of the dicke model in cavity qed: A counter-no-go statement, Phys. Rev. A 86, 053807 (2012)

    2012

  71. [71]

    T. L. Nguyen, J. M. Raimond, C. Sayrin, R. Corti˜ nas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, T. Jolicoeur, and M. Brune, Towards quantum simulation with circular rydberg atoms, Phys. Rev. X8, 011032 (2018)

    2018

  72. [72]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin sys- tems with trapped ions, Rev. Mod. Phys.93, 025001 (2021)

    2021

  73. [73]

    Zhang, L

    Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, Quantum phases in circuit qed with a supercon- ducting qubit array, Scientific Reports4, 4083 (2014)

    2014

  74. [74]

    De Bernardis, T

    D. De Bernardis, T. Jaako, and P. Rabl, Cavity quan- tum electrodynamics in the nonperturbative regime, Phys. Rev. A97, 043820 (2018)

    2018

  75. [75]

    Cortese, L

    E. Cortese, L. Garziano, and S. De Liberato, Polariton spectrum of the dicke-ising model, Phys. Rev. A96, 053861 (2017)

    2017

  76. [76]

    S. Sur, Y. Wang, M. Mahankali, S. Paschen, and Q. Si, Amplified response of cavity-coupled quantum-critical systems, Nature Communications17, 4404 (2026)

    2026

  77. [77]

    C. F. Lee and N. F. Johnson, First-order superradiant phase transitions in a multiqubit cavity system, Phys. Rev. Lett.93, 083001 (2004)

    2004

  78. [78]

    Gammelmark and K

    S. Gammelmark and K. Mølmer, Interacting spins in a cavity: Finite-size effects and symmetry-breaking dy- namics, Phys. Rev. A85, 042114 (2012)

    2012

  79. [79]

    Whitlock, A

    S. Whitlock, A. W. Glaetzle, and P. Hannaford, Sim- ulating quantum spin models using rydberg-excited atomic ensembles in magnetic microtrap arrays, Journ. Phys. B50, 074001 (2017)

    2017

  80. [80]

    Browaeys, D

    A. Browaeys, D. Barredo, and T. Lahaye, Experimen- tal investigations of dipole–dipole interactions between a few rydberg atoms, Journal of Physics B: Atomic, Molecular and Optical Physics49, 152001 (2016)

    2016

Showing first 80 references.