Pith. sign in

REVIEW 1 cited by

Thermalization from quantum entanglement: jet simulations in the massive Schwinger model

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2506.14983 v1 pith:ELUTWPR2 submitted 2025-06-17 hep-ph hep-thnucl-thquant-ph

classification hep-phhep-thnucl-thquant-ph
keywords quantumthermalizationmodelcomparedynamicsentanglementfield-theoreticmassive
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We investigate the emergence of thermalization in a quantum field-theoretic model mimicking the production of jets in QCD -- the massive Schwinger model coupled to external sources. Specifically, we compute the expectation values of local operators as functions of time and compare them to their thermal counterparts, quantify the overlap between the evolving density matrix and the thermal one, and compare the dynamics of the energy-momentum tensor to predictions from relativistic hydrodynamics. Through these studies, we find that the system approaches thermalization at late times and elucidate the mechanisms by which quantum entanglement drives thermalization in closed field-theoretic systems. Our results show how thermodynamic behavior emerges in real time from unitary quantum dynamics.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Deep inelastic scattering as a probe of entanglement: the complete QCD dipole cascade

    hep-ph 2026-07 conditional novelty 6.0 of 10

    The Shannon entropy of dipole multiplicities from the full Levin–Lublinsky equation in DIS reproduces the H1 hadron entropy, growing linearly with ln(1/x) and described by S = ln(2/3⟨n⟩) + 0.85.

Reference graph

Works this paper leans on

91 extracted references · 22 canonical work pages · cited by 1 Pith paper

  1. [1]

    Exact diagonalization Thermal expectation values of local operators can be obtained in the lattice Schwinger model using different Hamiltonian approaches. For sufficiently small systems, the exact spectrum of the Hamiltonian can be obtained using exact diagonalization: H|E n⟩=E n|En⟩.(B1) Note that here we discuss thermal properties of the Schwinger model...

  2. [2]

    We use the purification method to extract thermal expectation values of local observables [34–36]

    Purification and MPS In order to address the finite volume issue we perform finite temperature tensor network simulations for larger system sizes. We use the purification method to extract thermal expectation values of local observables [34–36]. A thermal system is described in terms of a density ma- trix rather than a state vector. In the tensor network ...

  3. [3]

    Construct the outer product Ψ A aαΨA∗ βb

  4. [4]

    SGibbs / N T [Ms] m/ g 0.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.0 0.1 0.2 0.3 0.4 0.5 0.6 1 / N SGibbs / N T=0.2/a T=0.3/a T=0.4/a T=0.5/a T=0.7/a T=1/a FIG

    0.2 0.4 0.6 0.8 1. SGibbs / N T [Ms] m/ g 0.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.0 0.1 0.2 0.3 0.4 0.5 0.6 1 / N SGibbs / N T=0.2/a T=0.3/a T=0.4/a T=0.5/a T=0.7/a T=1/a FIG. 12. Top panel: Gibbs entropy density for different values of the system sizeNas a function of temperature obtained with exact diagonalization as explained in the main text. Bo...

  5. [5]

    freeze-out time

    described in terms of a reduced density matrixρ A. We measure the distance of this reduced density matrix to thermal states, characterized by density matricesρ β, and determine a temperature by selecting the thermal state closest toρ A. To measure the proximity ofρ A and ρβ, different metrics can be used [46]. Two prominent measures of the distance betwee...

  6. [6]

    1.2 -6 -5 -4 -3 T [Ms] log10 error FIG

    0.2 0.4 0.6 0.8 1. 1.2 -6 -5 -4 -3 T [Ms] log10 error FIG. 14. Local observables (chiral condensate ¯ψψ, kinetic en- ergy densityKand condensate-condensate correlation func- tion ¯ψψ ¯ψψ) obtained with exact diagonalization (ED) and the purification algorithm realized with tensor network methods (TN) shown as a function of temperature. Inset: logarithm of...

  7. [7]

    0.5 1. 1.50. 0.2 0.4 0.6 0.8 1. 1.2 1/N2 Ms(N)- Ms(∞) [1/a] m= 10-3 10-2 FIG. 16. Masses of the first excited states shown for a variety of fermion mass valuesmas functions of the inverse square of the system sizeN. Linear fits for infinite volume extrapola- tion are shown in dashed lines. Infinite volume extrapolated values are subtracted. Fermion coup...

  8. [8]

    This achieves that all the tensors to the left/right ofAare in left/right canonical form; this is illus- trated by drawing diamonds for the tensors outside ofA

    Select a subregionAand choose the center of or- thogonality of the MPS to lie within this subregion. This achieves that all the tensors to the left/right ofAare in left/right canonical form; this is illus- trated by drawing diamonds for the tensors outside ofA

Show all 91 references
  1. [9]

    virtual space

    Drop the tensors outside ofA. It will be useful to think about the resulting object Ψ aα as a map be- tween the physical Hilbert spaceH A,dim(H A) = 2l and the “virtual space” of dimensionV,dim(V) = χ2. Latin letters are used to denote physical indices and Greek letters are us...

  2. [10]

    Dynamics of entanglement in expanding quantum fields,

    J. Berges, S. Floerchinger, and R. Venugopalan, “Dynamics of entanglement in expanding quantum fields,”JHEP04(2018) 145,arXiv:1712.09362 [hep-th]

  3. [11]

    physical

    An MPO representation of the reduced density ma- trix is shown on the left-hand side of the last row of Fig. 17. It is simply obtained by tracing over the virtual indices. One can in principle obtain the spectrum from this object by performing a SVD (SVD1), but this scales exp...

  4. [12]

    From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,”Adv. Phys. 65no. 3, (2016) 239–362,arXiv:1509.06411 [cond-mat.stat-mech]

  5. [13]

    Quantum chaos and thermalization in isolated systems of interacting particles,

    F. Borgonovi, F. M. Izrailev, L. F. Santos, and V. G. Zelevinsky, “Quantum chaos and thermalization in isolated systems of interacting particles,”Physics Reports626(2016) 1–58

  6. [14]

    Evolution of entanglement entropy in one-dimensional systems,

    P. Calabrese and J. Cardy, “Evolution of entanglement entropy in one-dimensional systems,”Journal of Statistical Mechanics: Theory and Experiment2005 no. 04, (Apr., 2005) P04010.http: //dx.doi.org/10.1088/1742-5468/2005/04/P04010

  7. [15]

    Quantum thermalization through entanglement in an isolated many-body system,

    A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,”Science353no. 6301, (2016) 794–800

  8. [16]

    Holographic derivation of entanglement entropy from AdS/CFT,

    S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,”Phys. Rev. Lett.96(2006) 181602,arXiv:hep-th/0603001

  9. [17]

    Holographic Entanglement Entropy: An Overview,

    T. Nishioka, S. Ryu, and T. Takayanagi, “Holographic Entanglement Entropy: An Overview,”J. Phys. A42 (2009) 504008,arXiv:0905.0932 [hep-th]

  10. [18]

    Entanglement entropy from a holographic viewpoint,

    T. Takayanagi, “Entanglement entropy from a holographic viewpoint,”Classical and Quantum Gravity 29no. 15, (2012) 153001

  11. [19]

    Quantum statistical mechanics in a closed system,

    J. M. Deutsch, “Quantum statistical mechanics in a closed system,”Phys. Rev. A43(Feb, 1991) 2046–2049. https: //link.aps.org/doi/10.1103/PhysRevA.43.2046

  12. [20]

    Chaos and Quantum Thermalization,

    M. Srednicki, “Chaos and Quantum Thermalization,” Phys. Rev. E50(3, 1994) ,arXiv:cond-mat/9403051

  13. [21]

    Jet energy loss and fragmentation in heavy ion collisions,

    D. E. Kharzeev and F. Loshaj, “Jet energy loss and fragmentation in heavy ion collisions,”Phys. Rev. D87 no. 7, (2013) 077501,arXiv:1212.5857 [hep-ph]

  14. [22]

    Thermal excitation spectrum from entanglement in an expanding quantum string,

    J. Berges, S. Floerchinger, and R. Venugopalan, “Thermal excitation spectrum from entanglement in an expanding quantum string,”Phys. Lett. B778(2018) 442–446,arXiv:1707.05338 [hep-ph]

  15. [23]

    and completely integrate out the gauge field using Gauss’s law which is possible for open boundary condi- tions2. We arrive at the following Hamiltonian in the fermionic basis: H(t) =H kin +H m +H E(t),(3) Hkin =− i 2a N−1X n=1 χ† nχn+1 −χ † n+1χn ,(4) Hm =m NX n=1 (−1)nχ† nχn...

  16. [24]

    Thermalization of Gauge Theories from their Entanglement Spectrum,

    N. Mueller, T. V. Zache, and R. Ott, “Thermalization of Gauge Theories from their Entanglement Spectrum,” Phys. Rev. Lett.129no. 1, (2022) 011601, arXiv:2107.11416 [quant-ph]

  17. [25]

    Weak ergodicity breaking in the Schwinger model,

    J.-Y. Desaules, D. Banerjee, A. Hudomal, Z. Papi´ c, A. Sen, and J. C. Halimeh, “Weak ergodicity breaking in the Schwinger model,”Phys. Rev. B107no. 20, (2023) L201105,arXiv:2203.08830 [cond-mat.str-el]

  18. [26]

    Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory,

    N. Mueller, T. Wang, O. Katz, Z. Davoudi, and M. Cetina, “Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory,”arXiv:2408.00069 [quant-ph]

  19. [27]

    SU(2) gauge theory in 2+1 dimensions on a plaquette chain obeys the eigenstate thermalization hypothesis,

    X. Yao, “SU(2) gauge theory in 2+1 dimensions on a plaquette chain obeys the eigenstate thermalization hypothesis,”Phys. Rev. D108no. 3, (2023) L031504, arXiv:2303.14264 [hep-lat]

  20. [28]

    Quantum thermalization of Quark-Gluon Plasma,

    S. Chen, L. Yan, and S. Shi, “Quantum thermalization of Quark-Gluon Plasma,”arXiv:2412.00662 [hep-ph]

  21. [29]

    Real-Time Nonperturbative Dynamics of Jet Production in Schwinger Model: Quantum Entanglement and Vacuum Modification,

    A. Florio, D. Frenklakh, K. Ikeda, D. Kharzeev, V. Korepin, S. Shi, and K. Yu, “Real-Time Nonperturbative Dynamics of Jet Production in Schwinger Model: Quantum Entanglement and Vacuum Modification,”Phys. Rev. Lett.131no. 2, (2023) 021902,arXiv:2301.11991 [hep-ph]

  22. [30]

    Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model,

    A. Florio, D. Frenklakh, K. Ikeda, D. E. Kharzeev, V. Korepin, S. Shi, and K. Yu, “Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model,”Phys. Rev. D110no. 9, (2024) 094029, arXiv:2404.00087 [hep-ph]

  23. [31]

    Vacuum polarization and the absence of free quarks,

    A. Casher, J. B. Kogut, and L. Susskind, “Vacuum polarization and the absence of free quarks,”Phys. Rev. D10(1974) 732–745

  24. [32]

    LPM effect as the origin of the jet fragmentation scaling in heavy ion collisions,

    F. Loshaj and D. E. Kharzeev, “LPM effect as the origin of the jet fragmentation scaling in heavy ion collisions,”Int. J. Mod. Phys. E21(2012) 1250088, arXiv:1111.0493 [hep-ph]

  25. [33]

    Universality and emergent effective fluid from jets and string breaking in the massive Schwinger model using tensor networks,

    R. A. Janik, M. A. Nowak, M. M. Rams, and I. Zahed, “Universality and emergent effective fluid from jets and string breaking in the massive Schwinger model using tensor networks,”arXiv:2502.12901 [hep-ph]

  26. [34]

    Strong Coupling Calculations of Lattice Gauge Theories: (1+1)-Dimensional Exercises,

    T. Banks, L. Susskind, and J. B. Kogut, “Strong Coupling Calculations of Lattice Gauge Theories: (1+1)-Dimensional Exercises,”Phys. Rev. D13(1976) 1043

  27. [35]

    Density-matrix algorithms for quantum renormalization groups,

    S. R. White, “Density-matrix algorithms for quantum renormalization groups,”Phys. Rev. B48(1993) 10345–10356

  28. [36]

    The density-matrix renormalization group,

    U. Schollwock, “The density-matrix renormalization group,”Rev. Mod. Phys.77(2005) 259–315, arXiv:cond-mat/0409292

  29. [37]

    Time-Dependent Variational Principle for Quantum Lattices,

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pizorn, H. Verschelde, and F. Verstraete, “Time-Dependent Variational Principle for Quantum Lattices,”Phys. Rev. Lett.107(2011) 070601,arXiv:1103.0936 [cond-mat.str-el]

  30. [38]

    Unifying time evolution and optimization with matrix product states,

    J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, “Unifying time evolution and optimization with matrix product states,”Phys. Rev. B 94no. 16, (2016) 165116

  31. [39]

    The mass spectrum of the Schwinger model with Matrix Product States,

    M. C. Ba˜ nuls, K. Cichy, K. Jansen, and J. I. Cirac, “The mass spectrum of the Schwinger model with Matrix Product States,”JHEP11(2013) 158, arXiv:1305.3765 [hep-lat]

  32. [40]

    Matrix product states for gauge field theories,

    B. Buyens, J. Haegeman, K. Van Acoleyen, H. Verschelde, and F. Verstraete, “Matrix product states for gauge field theories,”Phys. Rev. Lett.113 (2014) 091601,arXiv:1312.6654 [hep-lat]

  33. [41]

    Thermal evolution of the Schwinger model with Matrix Product Operators,

    M. C. Ba˜ nuls, K. Cichy, J. I. Cirac, K. Jansen, and H. Saito, “Thermal evolution of the Schwinger model with Matrix Product Operators,”Phys. Rev. D92 no. 3, (2015) 034519,arXiv:1505.00279 [hep-lat]

  34. [42]

    Real-time scattering in the lattice Schwinger model,

    I. Papaefstathiou, J. Knolle, and M. C. Ba˜ nuls, “Real-time scattering in the lattice Schwinger model,” arXiv:2402.18429 [hep-lat]

  35. [43]

    The ITensor Software Library for Tensor Network Calculations,

    M. Fishman, S. R. White, and E. M. Stoudenmire, 19 “The ITensor Software Library for Tensor Network Calculations,”SciPost Phys. Codebases(2022) 4. https://scipost.org/10.21468/SciPostPhysCodeb.4

  36. [44]

    Codebase release 0.3 for ITensor,

    M. Fishman, S. R. White, and E. M. Stoudenmire, “Codebase release 0.3 for ITensor,”SciPost Phys. Codebases(2022) 4–r0.3.https: //scipost.org/10.21468/SciPostPhysCodeb.4-r0.3

  37. [45]

    Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems,

    F. Verstraete, J. J. Garc ´ ıa-Ripoll, and J. I. Cirac, “Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems,”Phys. Rev. Lett.93no. 20, (2004) 207204

  38. [46]

    Mixed-State Dynamics in One-Dimensional Quantum Lattice Systems: A Time-Dependent Superoperator Renormalization Algorithm,

    M. Zwolak and G. Vidal, “Mixed-State Dynamics in One-Dimensional Quantum Lattice Systems: A Time-Dependent Superoperator Renormalization Algorithm,”Phys. Rev. Lett.93no. 20, (2004) 207205

  39. [47]

    Finite-temperature density matrix renormalization using an enlarged Hilbert space,

    A. E. Feiguin and S. R. White, “Finite-temperature density matrix renormalization using an enlarged Hilbert space,”Phys. Rev. B72no. 22, (2005) 220401

  40. [48]

    Charge Shielding and Quark Confinement in the Massive Schwinger Model,

    S. R. Coleman, R. Jackiw, and L. Susskind, “Charge Shielding and Quark Confinement in the Massive Schwinger Model,”Annals Phys.93(1975) 267

  41. [49]

    Area laws for the entanglement entropy - a review,

    J. Eisert, M. Cramer, and M. B. Plenio, “Area laws for the entanglement entropy - a review,”Rev. Mod. Phys. 82(2010) 277–306,arXiv:0808.3773 [quant-ph]

  42. [50]

    Volume-Law Entanglement Entropy of Typical Pure Quantum States,

    E. Bianchi, L. Hackl, M. Kieburg, M. Rigol, and L. Vidmar, “Volume-Law Entanglement Entropy of Typical Pure Quantum States,”PRX Quantum3no. 3, (2022) 030201,arXiv:2112.06959 [quant-ph]

  43. [51]

    Universality in volume-law entanglement of scrambled pure quantum states,

    Y. O. Nakagawa, M. Watanabe, S. Sugiura, and H. Fujita, “Universality in volume-law entanglement of scrambled pure quantum states,”Nature Commun.9 no. 1, (2018) 1635,arXiv:1703.02993 [cond-mat.stat-mech]

  44. [52]

    Thermal radiation and entanglement in proton-proton collisions at energies available at the CERN Large Hadron Collider,

    O. K. Baker and D. E. Kharzeev, “Thermal radiation and entanglement in proton-proton collisions at energies available at the CERN Large Hadron Collider,”Phys. Rev. D98no. 5, (2018) 054007,arXiv:1712.04558 [hep-ph]

  45. [53]

    Einstein-Podolsky-Rosen Paradox and Quantum Entanglement at Subnucleonic Scales,

    Z. Tu, D. E. Kharzeev, and T. Ullrich, “Einstein-Podolsky-Rosen Paradox and Quantum Entanglement at Subnucleonic Scales,”Phys. Rev. Lett. 124no. 6, (2020) 062001,arXiv:1904.11974 [hep-ph]

  46. [54]

    Gibbs entropy from entanglement in electric quenches,

    A. Florio and D. E. Kharzeev, “Gibbs entropy from entanglement in electric quenches,”Phys. Rev. D104 no. 5, (2021) 056021,arXiv:2106.00838 [hep-th]

  47. [55]

    Entanglement in a holographic Schwinger pair with confinement,

    S. Grieninger, D. E. Kharzeev, and I. Zahed, “Entanglement in a holographic Schwinger pair with confinement,”Phys. Rev. D108no. 8, (2023) 086030, arXiv:2305.07121 [hep-th]

  48. [56]

    Entanglement entropy in a time-dependent holographic Schwinger pair creation,

    S. Grieninger, D. E. Kharzeev, and I. Zahed, “Entanglement entropy in a time-dependent holographic Schwinger pair creation,”Phys. Rev. D108 no. 12, (2023) 126014,arXiv:2310.12042 [hep-th]

  49. [57]

    Wishart and random density matrices: Analytical results for the mean-square hilbert-schmidt distance,

    S. Kumar, “Wishart and random density matrices: Analytical results for the mean-square hilbert-schmidt distance,”Phys. Rev. A102(Jul, 2020) 012405.https: //link.aps.org/doi/10.1103/PhysRevA.102.012405

  50. [58]

    Fidelity for Mixed Quantum States,

    R. Jozsa, “Fidelity for Mixed Quantum States,”J. Mod. Opt.41no. 12, (1994) 2315–2323

  51. [59]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information. Cambridge University Press, 6, 2012

  52. [60]

    Entanglement measures and purification procedures,

    V. Vedral and M. B. Plenio, “Entanglement measures and purification procedures,”Phys. Rev. A57(1998) 1619–1633,arXiv:quant-ph/9707035

  53. [61]

    Experimental measurement of Hilbert-Schmidt distance between two-qubit states as means for speeding-up machine learning,

    V. Tr´ avn ´ ıˇ cek, K. Bartkiewicz, A.ˇCernoch, and K. Lemr, “Experimental measurement of Hilbert-Schmidt distance between two-qubit states as means for speeding-up machine learning,”Phys. Rev. Lett.123 (2019) 260501,arXiv:1907.02292 [quant-ph]

  54. [62]

    Variational quantum state diagonalization,

    R. LaRose, A. Tikku, ´E. O’Neel-Judy, L. Cincio, and P. J. Coles, “Variational quantum state diagonalization,”npj Quantum Information5no. 1, (2019) 57

  55. [63]

    Variational consistent histories as a hybrid algorithm for quantum foundations,

    A. Arrasmith, L. Cincio, A. T. Sornborger, W. H. Zurek, and P. J. Coles, “Variational consistent histories as a hybrid algorithm for quantum foundations,”Nature communications10no. 1, (2019) 3438

  56. [64]

    Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing,

    M. Cerezoet al., “Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing,” arXiv:2312.09121 [quant-ph]

  57. [65]

    How to enhance quantum generative adversarial learning of noisy information,

    P. Braccia, F. Caruso, and L. Banchi, “How to enhance quantum generative adversarial learning of noisy information,”New Journal of Physics23no. 5, (May,

  58. [66]

    Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma,

    P. M. Chesler and L. G. Yaffe, “Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma,”Phys. Rev. Lett.102(2009) 211601,arXiv:0812.2053 [hep-th]

  59. [67]

    Strong bound between trace distance and hilbert-schmidt distance for low-rank states,

    P. J. Coles, M. Cerezo, and L. Cincio, “Strong bound between trace distance and hilbert-schmidt distance for low-rank states,”Phys. Rev. A100(Aug, 2019) 022103. https: //link.aps.org/doi/10.1103/PhysRevA.100.022103

  60. [68]

    Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments,

    A. Jaiswal and V. Roy, “Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments,”Adv. High Energy Phys.2016(2016) 9623034,arXiv:1605.08694 [nucl-th]

  61. [69]

    New theories of relativistic hydrodynamics in the LHC era,

    W. Florkowski, M. P. Heller, and M. Spalinski, “New theories of relativistic hydrodynamics in the LHC era,” Rept. Prog. Phys.81no. 4, (2018) 046001, arXiv:1707.02282 [hep-ph]. [58]CMSCollaboration, S. Chatrchyanet al., “Observation of Long-Range Near-Side Angular Correlations ...

  62. [70]

    Small System Collectivity in Relativistic Hadronic and Nuclear Collisions,

    J. L. Nagle and W. A. Zajc, “Small System Collectivity in Relativistic Hadronic and Nuclear Collisions,”Ann. Rev. Nucl. Part. Sci.68(2018) 211–235, arXiv:1801.03477 [nucl-ex]

  63. [71]

    The smallest fluid on Earth,

    B. Schenke, “The smallest fluid on Earth,”Rept. Prog. Phys.84no. 8, (2021) 082301,arXiv:2102.11189 [nucl-th]

  64. [72]

    Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation,

    F. Turro and X. Yao, “Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation,” Phys. Rev. D111no. 9, (2025) 094502, arXiv:2502.17551 [hep-ph]

  65. [73]

    The M.I.T. Bag Model,

    K. Johnson, “The M.I.T. Bag Model,”Acta Phys. Polon. B6(1975) 865

  66. [74]

    Hybrid star within the 20 framework of a lowest-order constraint variational method,

    S. Khanmohamadi, H. R. Moshfegh, and S. Atashbar Tehrani, “Hybrid star within the 20 framework of a lowest-order constraint variational method,”Phys. Rev. D101no. 2, (2020) 023004, arXiv:1907.12029 [nucl-th]

  67. [75]

    Entanglement as a Probe of Hadronization,

    J. Datta, A. Deshpande, D. E. Kharzeev, C. J. Na ¨ ım, and Z. Tu, “Entanglement as a Probe of Hadronization,”Phys. Rev. Lett.134no. 11, (2025) 111902,arXiv:2410.22331 [hep-ph]

  68. [76]

    Boost-invariant early time dynamics from ads/cft,

    G. Beuf, M. P. Heller, R. A. Janik, and R. Peschanski, “Boost-invariant early time dynamics from ads/cft,” Journal of High Energy Physics2009no. 10, (Oct.,

  69. [77]

    Quasifragmentation functions in the massive Schwinger model,

    S. Grieninger and I. Zahed, “Quasifragmentation functions in the massive Schwinger model,”Phys. Rev. D110no. 11, (2024) 116009,arXiv:2406.01891 [hep-ph]

  70. [78]

    Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory,

    P. M. Chesler and L. G. Yaffe, “Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory,” Phys. Rev. D82(2010) 026006,arXiv:0906.4426 [hep-th]

  71. [79]

    Characteristics of thermalization of boost-invariant plasma from holography,

    M. P. Heller, R. A. Janik, and P. Witaszczyk, “Characteristics of thermalization of boost-invariant plasma from holography,”Physical Review Letters108 no. 20, (May, 2012) .http: //dx.doi.org/10.1103/PhysRevLett.108.201602

  72. [80]

    Numerical relativity approach to the initial value problem in asymptotically anti–de sitter spacetime for plasma thermalization: An adm formulation,

    M. P. Heller, R. A. Janik, and P. Witaszczyk, “Numerical relativity approach to the initial value problem in asymptotically anti–de sitter spacetime for plasma thermalization: An adm formulation,”Phys. Rev. D85(Jun, 2012) 126002.https: //link.aps.org/doi/10.1103/PhysRevD.85.126002

  73. [81]

    Fluid dynamics of heavy ion collisions with mode expansion,

    S. Floerchinger, E. Grossi, and J. Lion, “Fluid dynamics of heavy ion collisions with mode expansion,”Phys. Rev. C100no. 1, (2019) 014905,arXiv:1811.01870 [nucl-th]

  74. [82]

    Global fluid fits to identified particle transverse momentum spectra from heavy-ion collisions at the Large Hadron Collider,

    D. Devetak, A. Dubla, S. Floerchinger, E. Grossi, S. Masciocchi, A. Mazeliauskas, and I. Selyuzhenkov, “Global fluid fits to identified particle transverse momentum spectra from heavy-ion collisions at the Large Hadron Collider,”JHEP06(2020) 044, arXiv:1909.10485 [hep-ph]

  75. [83]

    Fluid dynamics of charm quarks in the quark-gluon plasma,

    F. Capellino, A. Dubla, S. Floerchinger, E. Grossi, A. Kirchner, and S. Masciocchi, “Fluid dynamics of charm quarks in the quark-gluon plasma,”Phys. Rev. D 108no. 11, (2023) 116011,arXiv:2307.14449 [hep-ph]

  76. [84]

    Multiplicity scaling in ideal and viscous hydrodynamics,

    H. Song and U. W. Heinz, “Multiplicity scaling in ideal and viscous hydrodynamics,”Phys. Rev. C78(2008) 024902,arXiv:0805.1756 [nucl-th]

  77. [86]

    Quasiparton distributions in massive QED2: Toward quantum computation,

    S. Grieninger, K. Ikeda, and I. Zahed, “Quasiparton distributions in massive QED2: Toward quantum computation,”Phys. Rev. D110no. 7, (2024) 076008, arXiv:2404.05112 [hep-ph]

  78. [88]

    Equipartition of the entanglement entropy,

    J. C. Xavier, F. C. Alcaraz, and G. Sierra, “Equipartition of the entanglement entropy,”Phys. Rev. B98no. 4, (2018) 041106,arXiv:1804.06357 [cond-mat.stat-mech]

  79. [89]

    Entanglement equipartition in critical random spin chains,

    X. Turkeshi, P. Ruggiero, V. Alba, and P. Calabrese, “Entanglement equipartition in critical random spin chains,”Phys. Rev. B102no. 1, (2020) 014455, arXiv:2005.03331 [cond-mat.stat-mech]

  80. [90]

    Symmetry-resolved entanglement in many-body systems,

    M. Goldstein and E. Sela, “Symmetry-resolved entanglement in many-body systems,”Phys. Rev. Lett. 120no. 20, (2018) 200602,arXiv:1711.09418 [cond-mat.stat-mech]

  81. [91]

    Entanglement and symmetry resolution in two dimensional free quantum field theories,

    S. Murciano, G. Di Giulio, and P. Calabrese, “Entanglement and symmetry resolution in two dimensional free quantum field theories,”JHEP08 (2020) 073,arXiv:2006.09069 [hep-th]

  82. [2009]

    http://dx.doi.org/10.1088/1126-6708/2009/10/043

    043–043. http://dx.doi.org/10.1088/1126-6708/2009/10/043

  83. [2021]

    https://dx.doi.org/10.1088/1367-2630/abf798

    053024. https://dx.doi.org/10.1088/1367-2630/abf798

Pith tools