Kogut, J. B. The lattice gauge theory approach to quantum chromodynamics. Rev. Mod. Phys. 55, 775 (1983).
Greensite, J. The confinement problem in lattice gauge theory. Prog. Part. Nucl. Phys. 51, 1–83 (2003).
Sachdev, S. Emergent gauge fields and the high-temperature superconductors. Philos. Trans. A 374, 20150248 (2016).
Scherg, S. et al. Observing non-ergodicity due to kinetic constraints in tilted Fermi–Hubbard chains. Nat. Commun. 12, 4490 (2021).
Kohlert, T. et al. Exploring the regime of fragmentation in strongly tilted Fermi–Hubbard chains. Phys. Rev. Lett. 130, 010201 (2023).
Adler, D. et al. Observation of Hilbert space fragmentation and fractonic excitations in 2D. Nature 636, 80 (2024).
Kim, K., Yang, F., Mølmer, K. & Ahn, J. Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays. Phys. Rev. X 14, 011025 (2024).
Zhao, L., Datla, P. R., Tian, W., Aliyu, M. M. & Loh, H. Observation of quantum thermalization restricted to Hilbert space fragments and \({{\mathbb{Z}}}_{2k}\) scars. Phys. Rev. X 15, 011035 (2025).
Honda, K. et al. Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose–Hubbard chains. Sci. Adv. 11, eadv3255 (2025).
Gonzalez-Cuadra, D. et al. Observation of string breaking on a (2 + 1)D Rydberg quantum simulator. Nature 642, 321–326 (2025).
Tagliacozzo, L., Celi, A., Orland, P. & Lewenstein, M. Simulations of non-Abelian gauge theories with optical lattices. Nat. Commun. 4, 2615 (2013).
Banerjee, D. et al. Atomic quantum simulation of dynamical gauge fields coupled to Fermionic matter: from string breaking to evolution after a quench. Phys. Rev. Lett. 109, 175302 (2012).
Bañuls, M. C. et al. Simulating lattice gauge theories within quantum technologies. Eur. Phys. J. D 74, 165 (2020).
Zohar, E., Cirac, J. I. & Reznik, B. Cold-atom quantum simulator for SU(2) Yang–Mills lattice gauge theory. Phys. Rev. Lett. 110, 125304 (2013).
Schweizer, C. et al. Floquet approach to \({{\mathbb{Z}}}_{2}\) lattice gauge theories with ultracold atoms in optical lattices. Nat. Phys. 15, 1168–1173 (2019).
Zhou, Z.-Y. et al. Thermalization dynamics of a gauge theory on a quantum simulator. Science 377, 311–314 (2022).
Halimeh, J. C., Aidelsburger, M., Grusdt, F., Hauke, P. & Yang, B. Cold-atom quantum simulators of gauge theories. Nat. Phys. 21, 25–36 (2025).
Surace, F. M. et al. Lattice gauge theories and string dynamics in Rydberg atom quantum simulators. Phys. Rev. X 10, 021041 (2020).
Bauer, C. W., Davoudi, Z., Klco, N. & Savage, M. J. Quantum simulation of fundamental particles and forces. Nat. Rev. Phys. 5, 420–432 (2023).
Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).
Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).
Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).
Turner, C. J., Michailidis, A. A., Abanin, D. A., Serbyn, M. & Papić, Z. Weak ergodicity breaking from quantum many-body scars. Nat. Phys. 14, 745–749 (2018).
Smith, A., Knolle, J., Moessner, R. & Kovrizhin, D. L. Dynamical localization in \({{\mathbb{Z}}}_{2}\) lattice gauge theories. Phys. Rev. B 97, 245137 (2018).
Karpov, P., Verdel, R., Huang, Y.-P., Schmitt, M. & Heyl, M. Disorder-free localization in an interacting 2D lattice gauge theory. Phys. Rev. Lett. 126, 130401 (2021).
Banerjee, D. & Sen, A. Quantum scars from zero modes in an Abelian lattice gauge theory on ladders. Phys. Rev. Lett. 126, 220601 (2021).
Aramthottil, A. S. et al. Scar states in deconfined \({{\mathbb{Z}}}_{2}\) lattice gauge theories. Phys. Rev. B 106, L041101 (2022).
Halimeh, J. C., Barbiero, L., Hauke, P., Grusdt, F. & Bohrdt, A. Robust quantum many-body scars in lattice gauge theories. Quantum 7, 1004 (2023).
Desaules, J.-Y. et al. Weak ergodicity breaking in the Schwinger model. Phys. Rev. B 107, L201105 (2023).
Desaules, J.-Y. et al. Prominent quantum many-body scars in a truncated Schwinger model. Phys. Rev. B 107, 205112 (2023).
Gyawali, G. et al. Observation of disorder-free localization and efficient disorder averaging on a quantum processor. Preprint at https://arxiv.org/abs/2410.06557 (2024).
Morong, W. et al. Observation of Stark many-body localization without disorder. Nature 599, 393–398 (2021).
Sala, P., Rakovszky, T., Verresen, R., Knap, M. & Pollmann, F. Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians. Phys. Rev. X 10, 011047 (2020).
Khemani, V., Hermele, M. & Nandkishore, R. Localization from Hilbert space shattering: From theory to physical realizations. Phys. Rev. B 101, 174204 (2020).
Yang, Z.-C., Liu, F., Gorshkov, A. V. & Iadecola, T. Hilbert-space fragmentation from strict confinement. Phys. Rev. Lett. 124, 207602 (2020).
Jeyaretnam, J., Bhore, T., Osborne, J. J., Halimeh, J. C. & Papić, Z. Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model. Commun. Phys. 8, 172 (2025).
Desaules, J.-Y. et al. Ergodicity breaking under confinement in cold-atom quantum simulators. Quantum 8, 1274 (2024).
Ciavarella, A. N., Bauer, C. W. & Halimeh, J. C. Generic Hilbert space fragmentation in Kogut–Susskind lattice gauge theories. Phys. Rev. D 112, L091501 (2025).
Wang, Y.-Y. et al. Exploring Hilbert-space fragmentation on a superconducting processor. PRX Quantum 6, 010325 (2025).
Karch, S. et al. Probing quantum many-body dynamics using subsystem Loschmidt echos. Preprint at https://arxiv.org/abs/2501.16995 (2025).
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).
Deutsch, J. M. Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046 (1991).
Rigol, M., Dunjko, V. & Olshanii, M. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008).
Rakovszky, T., Sala, P., Verresen, R., Knap, M. & Pollmann, F. Statistical localization: from strong fragmentation to strong edge modes. Phys. Rev. B 101, 125126 (2020).
Chandran, A., Kim, I. H., Vidal, G. & Abanin, D. A. Constructing local integrals of motion in the many-body localized phase. Phys. Rev. B 91, 085425 (2015).
Imbrie, J. Z., Ros, V. & Scardicchio, A. Local integrals of motion in many-body localized systems. Ann. Phys. (Berlin) 529, 1600278 (2017).
Rademaker, L., Ortuño, M. & Somoza, A. M. Many-body localization from the perspective of integrals of motion. Ann. Phys. 529, 1600322 (2017).
Singh, H., Ware, B., Vasseur, R. & Gopalakrishnan, S. Local integrals of motion and the quasiperiodic many-body localization transition. Phys. Rev. B 103, L220201 (2021).
Ros, V., Müller, M. & Scardicchio, A. Integrals of motion in the many-body localized phase. Nucl. Phys. B 891, 420–465 (2015).
Bertoni, C., Eisert, J., Kshetrimayum, A., Nietner, A. & Thomson, S. Local integrals of motion and the stability of many-body localization in Wannier-Stark potentials. Phys. Rev. B 109, 024206 (2024).
Wahl, T. B. & Béri, B. Local integrals of motion for topologically ordered many-body localized systems. Phys. Rev. Res. 2, 033099 (2020).
Marcuzzi, M. et al. Facilitation dynamics and localization phenomena in Rydberg lattice gases with position disorder. Phys. Rev. Lett. 118, 063606 (2017).
Magoni, M., Mazza, P. P. & Lesanovsky, I. Emergent Bloch oscillations in a kinetically constrained Rydberg spin lattice. Phys. Rev. Lett. 126, 103002 (2021).
Hart, O. Exact Mazur bounds in the pair-flip model and beyond. SciPost Phys. 7, 040 (2024).
Hahn, D., McClarty, P. A. & Luitz, D. J. Information dynamics in a model with Hilbert space fragmentation. SciPost Phys. 11, 074 (2021).
Choi, J. et al. Preparing random states and benchmarking with many-body quantum chaos. Nature 613, 468–473 (2023).
Pilatowsky-Cameo, S., Dag, C. B., Ho, W. W. & Choi, S. Complete Hilbert-space ergodicity in quantum dynamics of generalized Fibonacci drives. Phys. Rev. Lett. 131, 250401 (2023).
Pilatowsky-Cameo, S., Marvian, I., Choi, S. & Ho, W. W. Hilbert-space ergodicity in driven quantum systems: obstructions and designs. Phys. Rev. X 14, 041059 (2024).
Ghosh, S., Langlett, C. M., Hunter-Jones, N. & Rodriguez-Nieva, J. F. Late-time ensembles of quantum states in quantum chaotic systems. Phys. Rev. B 112, 094302 (2025).
Le, Y., Zhang, Y., Gopalakrishnan, S., Rigol, M. & Weiss, D. S. Observation of hydrodynamization and local prethermalization in 1D Bose gases. Nature 618, 494–499 (2023).
Fendley, P. Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain. J. Phys. A 49, 30LT01 (2016).
Olund, C. T., Yao, N. Y. & Kemp, J. Boundary strong zero modes. Phys. Rev. B 111, L201114 (2025).
Else, D. V., Fendley, P., Kemp, J. & Nayak, C. Prethermal strong zero modes and topological qubits. Phys. Rev. X 7, 041062 (2017).
Kempkes, S. et al. Robust zero-energy modes in an electronic higher-order topological insulator. Nat. Mater. 18, 1292–1297 (2019).
Verresen, R., Jones, N. G. & Pollmann, F. Topology and edge modes in quantum critical chains. Phys. Rev. Lett. 120, 057001 (2018).
Verresen, R., Thorngren, R., Jones, N. G. & Pollmann, F. Gapless topological phases and symmetry-enriched quantum criticality. Phys. Rev. X 11, 041059 (2021).
Morningstar, A., Khemani, V. & Huse, D. A. Kinetically constrained freezing transition in a dipole-conserving system. Phys. Rev. B 101, 214205 (2020).
Wang, C. & Yang, Z.-C. Freezing transition in the particle-conserving East model. Phys. Rev. B 108, 144308 (2023).
Pozderac, C., Speck, S., Feng, X., Huse, D. A. & Skinner, B. Exact solution for the filling-induced thermalization transition in a one-dimensional fracton system. Phys. Rev. B 107, 045137 (2023).
Classen-Howes, J., Senese, R. & Prakash, A. Universal freezing transitions of dipole-conserving chains. Phys. Rev. B 112, 125148 (2025).
Tian, W. et al. Parallel assembly of arbitrary defect-free atom arrays with a multitweezer algorithm. Phys. Rev. Applied 19, 034048 (2023).
Labuhn, H. et al. Single-atom addressing in microtraps for quantum-state engineering using Rydberg atoms. Phys. Rev. A 90, 023415 (2014).
Yang, F., Yarloo, H., Zhang, H.-C., Mølmer, K. & Nielsen, A. E. Probing Hilbert space fragmentation with strongly interacting Rydberg atoms. Phys. Rev. B 111, 144313 (2025).
Bravyi, S., DiVincenzo, D. P. & Loss, D. Schrieffer–Wolff transformation for quantum many-body systems. Ann. Phys. 326, 2793–2826 (2011).
Bluvstein, D. et al. Controlling quantum many-body dynamics in driven Rydberg atom arrays. Science 371, 1355–1359 (2021).
Lesanovsky, I. & Katsura, H. Interacting Fibonacci anyons in a Rydberg gas. Phys. Rev. A 86, 041601 (2012).
Datla, P. R. et al. Dataset for ‘Statistical localization of U(1) lattice gauge theory in a Rydberg simulator’. Zenodo https://doi.org/10.5281/zenodo.18012627 (2026).