Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys. 83, 863–883 (2011).
Mitra, A. Quantum quench dynamics. Annu. Rev. Condens. Matter Phys. 9, 245–259 (2018).
Rudner, M. S. & Lindner, N. H. Band structure engineering and non-equilibrium dynamics in Floquet topological insulators. Nat. Rev. Phys. 2, 229–244 (2020).
Vasseur, R. & Moore, J. E. Nonequilibrium quantum dynamics and transport: from integrability to many-body localization. J. Stat. Mech. Theory Exp. 2016, 064010 (2016).
Rigol, M., Dunjko, V. & Olshanii, M. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008).
Heyl, M., Polkovnikov, A. & Kehrein, S. Dynamical quantum phase transitions in the transverse-field Ising model. Phys. Rev. Lett. 110, 135704 (2013).
Deutsch, J. M. Eigenstate thermalization hypothesis. Rep. Prog. Phys. 81, 082001 (2018).
Abanin, D., De Roeck, W., Ho, W. W. & Huveneers, F. A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems. Commun. Math. Phys. 354, 809–827 (2017).
Verstraete, F. & Cirac, J. I. Renormalization algorithms for quantum-many body systems in two and higher dimensions. Preprint at https://doi.org/10.48550/arXiv.cond-mat/0407066 (2004).
Park, G., Gray, J. & Chan, G. K.-L. Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation. Phys. Rev. B 112, 174310 (2025).
Wurtz, J. et al. Aquila: Quera’s 256-qubit neutral-atom quantum computer. Preprint at https://doi.org/10.48550/arXiv.2306.11727 (2023).
Hashizume, T., Herbort, F., Tindall, J. & Jaksch, D. Dynamical quantum phase transitions on random networks. N. J. Phys. 27, 064506 (2025).
Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nat. Phys. 11, 124–130 (2015).
Srednicki, M. Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994).
Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).
Papić, Z. Weak ergodicity breaking through the lens of quantum entanglement. In Entanglement in Spin Chains: From Theory to Quantum Technology Applications (eds Bayat, A. et al.) 341–395 https://doi.org/10.1007/978-3-031-03998-0_13 (Springer, 2022).
Landau, L. D. On the theory of phase transitions. Zh. Eksp. Teor. Fiz. 7, 19–32 (1937).
Sachdev, S. Quantum Phase Transitions 2nd edn https://doi.org/10.1017/CBO9780511973765 (Cambridge Univ. Press, 2011)
Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator. Nature 595, 227–232 (2021).
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).
Sengupta, K., Powell, S. & Sachdev, S. Quench dynamics across quantum critical points. Phys. Rev. A 69, 053616 (2004).
Cazalilla, M. A. Effect of suddenly turning on interactions in the Luttinger model. Phys. Rev. Lett. 97, 156403 (2006).
Titum, P., Iosue, J. T., Garrison, J. R., Gorshkov, A. V. & Gong, Z.-X. Probing ground-state phase transitions through quench dynamics. Phys. Rev. Lett. 123, 115701 (2019).
Titum, P. & Maghrebi, M. F. Nonequilibrium criticality in quench dynamics of long-range spin models. Phys. Rev. Lett. 125, 040602 (2020).
Karrasch, C. & Schuricht, D. Dynamical phase transitions after quenches in nonintegrable models. Phys. Rev. B 87, 195104 (2013).
Zvyagin, A. A. Dynamical quantum phase transitions (review article). Low Temp. Phys. 42, 971–994 (2016).
Halimeh, J. C. et al. Prethermalization and persistent order in the absence of a thermal phase transition. Phys. Rev. B 95, 024302 (2017).
Žunkovič, B., Heyl, M., Knap, M. & Silva, A. Dynamical quantum phase transitions in spin chains with long-range interactions: merging different concepts of nonequilibrium criticality. Phys. Rev. Lett. 120, 130601 (2018).
Berges, J., Borsányi, S. & Wetterich, C. Prethermalization. Phys. Rev. Lett. 93, 142002 (2004).
Mori, T., Ikeda, T. N., Kaminishi, E. & Ueda, M. Thermalization and prethermalization in isolated quantum systems: a theoretical overview. J. Phys. B 51, 112001 (2018).
Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).
Bluvstein, D. et al. Controlling quantum many-body dynamics in driven Rydberg atom arrays. Science 371, 1355–1359 (2021).
Smale, S. et al. Observation of a transition between dynamical phases in a quantum degenerate Fermi gas. Sci. Adv. 5, eaax1568 (2019).
Muniz, J. A. et al. Exploring dynamical phase transitions with cold atoms in an optical cavity. Nature 580, 602–607 (2020).
Chu, A., Will, J., Arlt, J., Klempt, C. & Rey, A. M. Simulation of xxz spin models using sideband transitions in trapped bosonic gases. Phys. Rev. Lett. 125, 240504 (2020).
Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).
De, A. et al. Non-equilibrium critical scaling and universality in a quantum simulator. Nat. Commun. 16, 7939 (2025).
Keesling, A. et al. Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator. Nature 568, 207–211 (2019).
Castelnovo, C., Moessner, R. & Sondhi, S. Spin ice, fractionalization, and topological order. Annu. Rev. Condens. Matter Phys. 3, 35–55 (2012).
Nandkishore, R. M. & Hermele, M. Fractons. Annu. Rev. Condens. Matter Phys. 10, 295–313 (2019).
Moudgalya, S., Bernevig, B. A. & Regnault, N. Quantum many-body scars and Hilbert space fragmentation: a review of exact results. Rep. Prog. Phys. 85, 086501 (2022).
Katschke, L., Farrell, R. C., Borla, U., Pollet, L. & Halimeh, J. C. Finite-temperature dynamical phase diagram of the 2 + 1D quantum Ising model. Preprint at https://doi.org/10.48550/arXiv.2602.16772 (2026).
Reinić, N., Jaschke, D., Wanisch, D., Silvi, P. & Montangero, S. Finite-temperature Rydberg arrays: quantum phases and entanglement characterization. Phys. Rev. Res. 6, 033322 (2024).
Stoner, E. C. & Wohlfarth, E. P. A mechanism of magnetic hysteresis in heterogeneous alloys. Philos. Trans. R. Soc. Lond. Ser. A 240, 599–642 (1948).
Liu, F., Yang, Z.-C., Bienias, P., Iadecola, T. & Gorshkov, A. V. Localization and criticality in antiblockaded two-dimensional Rydberg atom arrays. Phys. Rev. Lett. 128, 013603 (2022).
Bluvstein, D. et al. A quantum processor based on coherent transport of entangled atom arrays. Nature 604, 451–456 (2022).
Swingle, B., Bentsen, G., Schleier-Smith, M. & Hayden, P. Measuring the scrambling of quantum information. Phys. Rev. A 94, 040302 (2016).
Daniel, A. et al. Bridging quantum criticality via many-body scarring. Phys. Rev. B 107, 235108 (2023).
Hudomal, A. et al. Driving quantum many-body scars in the PXP model. Phys. Rev. B 106, 104302 (2022).
Chertkov, E. et al. Characterizing a non-equilibrium phase transition on a quantum computer. Nat. Phys. 19, 1799–1804 (2023).
Iadecola, T., Wilson, J. H. & Pixley, J. Concomitant entanglement and control criticality driven by collective measurements. PRX Quantum 6, 010351 (2025).
Daley, A. J. et al. Practical quantum advantage in quantum simulation. Nature 607, 667–676 (2022).
Wendl, A. et al. Emergence of mesoscale quantum phase transitions in a ferromagnet. Nature 609, 65–70 (2022).
Jiang, X. et al. Using magnetic dynamics to measure the spin gap in a candidate Kitaev material. npj Quantum Mater. 10, 15 (2025).
Radovskaia, V. et al. Photoengineering the magnon spectrum in an insulating antiferromagnet. Nat. Phys. 22, 728–735 (2026).
González-Cuadra, D. et al. Observation of string breaking on a (2 + 1)D Rydberg quantum simulator. Nature 642, 321–326 (2025).
Bloqade.jl: package for the quantum computation and quantum simulation based on the neutral-atom architecture. GitHub https://github.com/QuEraComputing/Bloqade.jl/ (2023).
Perlmutter. NERSC https://www.nersc.gov/systems/perlmutter (2023).
Jaksch, D. et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208–2211 (2000).
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).
Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326, 96–192 (2011).
Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor software library for tensor network calculations. SciPost Phys. Codebases 4 https://doi.org/10.21468/SciPostPhysCodeb.4 (2022).
Lin, S.-H., Zaletel, M. P. & Pollmann, F. Efficient simulation of dynamics in two-dimensional quantum spin systems with isometric tensor networks. Phys. Rev. B 106, 245102 (2022).
Begušić, T. & Chan, G. K.-L. Real-time operator evolution in two and three dimensions via sparse Pauli dynamics. PRX Quantum 6, 020302 (2025).
Moeckel, M. & Kehrein, S. Interaction quench in the Hubbard model. Phys. Rev. Lett. 100, 175702 (2008).
Haghshenas, R. et al. Digital quantum magnetism on a trapped-ion quantum computer. Nature 653, 56–62 (2026).
Landau, L. D. & Lifshitz, E. M. Statistical Physics, Part 1 3rd edn, Course of Theoretical Physics Vol. 5 (Pergamon, 1980)
Heyl, M. Dynamical quantum phase transitions: a review. Rep. Prog. Phys. 81, 054001 (2018).
Xu, K. et al. Probing dynamical phase transitions with a superconducting quantum simulator. Sci. Adv. 6, eaba4935 (2020).
Hashizume, T., McCulloch, I. P. & Halimeh, J. C. Dynamical phase transitions in the two-dimensional transverse-field Ising model. Phys. Rev. Res. 4, 013250 (2022).
Karch, S. et al. Probing quantum many-body dynamics using subsystem Loschmidt echos. Preprint at https://doi.org/10.48550/arXiv.2501.16995 (2025).
Weinberg, P., Wu, K.-H., Long, J. & Luo, X.-Z. R. Queracomputing/bloqade-python: v0.15.11. Zenodo https://doi.org/10.5281/zenodo.11114110 (2024).
Ates, C., Pohl, T., Pattard, T. & Rost, J. M. Antiblockade in Rydberg excitation of an ultracold lattice gas. Phys. Rev. Lett. 98, 023002 (2007).
Osterholz, P. et al. Collective cluster nucleation dynamics in quantum magnets. Preprint at https://doi.org/10.48550/arXiv.2512.04656 (2026).
