Haldane, F. D. M. Many-particle translational symmetries of two-dimensional electrons at rational Landau-level filling. Phys. Rev. Lett. 55, 2095 https://doi.org/10.1103/PhysRevLett.55.2095 (1985).
Trugman, S. A. & Kivelson, S. Exact results for the fractional quantum Hall effect with general interactions. Phys. Rev. B 31, 5280 https://doi.org/10.1103/PhysRevB.31.5280 (1985).
Seidel, A., Fu, H., Lee, D.-H., Leinaas, J. M. & Moore, J. Incompressible quantum liquids and new conservation laws. Phys. Rev. Lett. 95, 266405 https://doi.org/10.1103/PhysRevLett.95.266405 (2005).
Moudgalya, S., Bernevig, B. A. & Regnault, N. Quantum many-body scars in a Landau level on a thin torus. Phys. Rev. B 102, 195150 https://doi.org/10.1103/PhysRevB.102.195150 (2020).
Zerba, C., Seidel, A., Pollmann, F. & Knap, M. Emergent fracton hydrodynamics of ultracold atoms in partially filled Landau levels. PRX Quantum 6, 020321 https://doi.org/10.1103/PRXQuantum.6.020321 (2025).
Wannier, G. H. Dynamics of band electrons in electric and magnetic fields. Rev. Mod. Phys. 34, 645 https://doi.org/10.1103/RevModPhys.34.645 (1962).
Sachdev, S., Sengupta, K. & Girvin, S. M. Mott insulators in strong electric fields. Phys. Rev. B 66, 075128 https://doi.org/10.1103/PhysRevB.66.075128 (2002).
Pretko, M. The fracton gauge principle. Phys. Rev. B 98, 115134 https://doi.org/10.1103/PhysRevB.98.115134 (2018).
Nandkishore, R. M. & Hermele, M. Fractons. Annu. Rev. Condens. Matter Phys. 10, 295 https://doi.org/10.1146/annurev-conmatphys-031218-013604 (2019).
Pretko, M., Chen, X. & You, Y. Fracton phases of matter. Int. J. Mod. Phys. A 35, 2030003 https://doi.org/10.1142/S0217751X20300033 (2020).
Gromov, A. & Radzihovsky, L. Colloquium: fracton matter. Rev. Mod. Phys. 96, 011001 https://doi.org/10.1103/RevModPhys.96.011001 (2024).
Chamon, C. Quantum glassiness in strongly correlated clean systems: an example of topological overprotection. Phys. Rev. Lett. 94, 040402 https://doi.org/10.1103/PhysRevLett.94.040402 (2005).
Schulz, M., Hooley, C. A., Moessner, R. & Pollmann, F. Stark many-body localization. Phys. Rev. Lett. 122, 040606 https://doi.org/10.1103/PhysRevLett.122.040606 (2019).
Morong, W. et al. Observation of Stark many-body localization without disorder. Nature 599, 393 https://doi.org/10.1038/s41586-021-03988-0 (2021).
Guo, Q. et al. Stark many-body localization on a superconducting quantum processor. Phys. Rev. Lett. 127, 240502 https://doi.org/10.1103/PhysRevLett.127.240502 (2021).
Gromov, A., Lucas, A. & Nandkishore, R. M. Fracton hydrodynamics. Phys. Rev. Res. 2, 033124 https://doi.org/10.1103/PhysRevResearch.2.033124 (2020).
Feldmeier, J., Sala, P., De Tomasi, G., Pollmann, F. & Knap, M. Anomalous diffusion in dipole- and higher-moment-conserving systems. Phys. Rev. Lett. 125, 245303 https://doi.org/10.1103/PhysRevLett.125.245303 (2020).
Morningstar, A., Khemani, V. & Huse, D. A. Kinetically constrained freezing transition in a dipole-conserving system. Phys. Rev. B 101, 214205 https://doi.org/10.1103/PhysRevB.101.214205 (2020).
Zhang, P. Subdiffusion in strongly tilted lattice systems. Phys. Rev. Res. 2, 033129 https://doi.org/10.1103/PhysRevResearch.2.033129 (2020).
Guardado-Sanchez, E., Morningstar, A., Spar, B. M., Brown, P. T., Huse, D. A. & Bakr, W. S. Subdiffusion and heat transport in a tilted two-dimensional Fermi–Hubbard system. Phys. Rev. X 10, 011042 https://doi.org/10.1103/PhysRevX.10.011042 (2020).
Feldmeier, J. & Knap, M. Critically slow operator dynamics in constrained many-body systems. Phys. Rev. Lett. 127, 235301 https://doi.org/10.1103/PhysRevLett.127.235301 (2021).
De Tomasi, G., Hetterich, D., Sala, P. & Pollmann, F. Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization. Phys. Rev. B 100, 214313 https://doi.org/10.1103/PhysRevB.100.214313 (2019).
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 https://doi.org/10.1103/PhysRevX.10.011047 (2020).
Yang, Z.-C., Liu, F., Gorshkov, A. V. & Iadecola, T. Hilbert-space fragmentation from strict confinement. Phys. Rev. Lett. 124, 207602 https://doi.org/10.1103/PhysRevLett.124.207602 (2020).
Khemani, V., Hermele, M. & Nandkishore, R. Localization from Hilbert space shattering: from theory to physical realizations. Phys. Rev. B 101, 174204 https://doi.org/10.1103/PhysRevB.101.174204 (2020).
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 https://doi.org/10.1088/1361-6633/ac73a0 (2022).
Will, M., Moessner, R. & Pollmann, F. Realization of Hilbert space fragmentation and fracton dynamics in two dimensions. Phys. Rev. Lett. 133, 196301 https://doi.org/10.1103/PhysRevLett.133.196301 (2024).
Stephen, D. T., Hart, O. & Nandkishore, R. M. Ergodicity breaking provably robust to arbitrary perturbations. Phys. Rev. Lett. 132, 040401 https://doi.org/10.1103/PhysRevLett.132.040401 (2024).
Honda, K. et al. Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose–Hubbard chains. Sci. Adv. 11, eadv3255 https://doi.org/10.1126/sciadv.adv3255 (2025).
Scherg, S. et al. Observing non-ergodicity due to kinetic constraints in tilted Fermi–Hubbard chains. Nat. Commun. 12, 4490 https://doi.org/10.1038/s41467-021-24726-0 (2021).
Kohlert, T. et al. Exploring the regime of fragmentation in strongly tilted Fermi–Hubbard chains. Phys. Rev. Lett. 130, 010201 https://doi.org/10.1103/PhysRevLett.130.010201 (2023).
Adler, D. et al. Observation of Hilbert space fragmentation and fractonic excitations in 2D. Nature 636, 80 https://doi.org/10.1038/s41586-024-08188-0 (2024).
Sengupta, K. Phases and dynamics of ultracold Bosons in a tilted optical lattice. in Entanglement in Spin Chains: From Theory to Quantum Technology Applications (eds Bayat, A., Bose, S. & Johannesson, H.) 425–458 https://doi.org/10.1007/978-3-031-03998-0_15 (Springer, 2022).
Lake, E., Hermele, M. & Senthil, T. Dipolar Bose–Hubbard model. Phys. Rev. B 106, 064511 https://doi.org/10.1103/PhysRevB.106.064511 (2022).
Zechmann, P., Altman, E., Knap, M. & Feldmeier, J. Fractonic Luttinger liquids and supersolids in a constrained Bose–Hubbard model. Phys. Rev. B 107, 195131 https://doi.org/10.1103/PhysRevB.107.195131 (2023).
Lake, E. & Senthil, T. Non-Fermi liquids from kinetic constraints in tilted optical lattices. Phys. Rev. Lett. 131, 043403 https://doi.org/10.1103/PhysRevLett.131.043403 (2023).
Lake, E., Lee, H.-Y., Han, J. H. & Senthil, T. Dipole condensates in tilted Bose–Hubbard chains. Phys. Rev. B 107, 195132 https://doi.org/10.1103/PhysRevB.107.195132 (2023).
Boesl, J., Zechmann, P., Feldmeier, J. & Knap, M. Deconfinement dynamics of fractons in tilted Bose–Hubbard chains. Phys. Rev. Lett. 132, 143401 https://doi.org/10.1103/PhysRevLett.132.143401 (2024).
Kale, A. et al. Schrieffer–Wolff transformations for experiments: dynamically suppressing virtual doublon–hole excitations in a Fermi–Hubbard simulator. Phys. Rev. A 106, 012428 https://doi.org/10.1103/PhysRevA.106.012428 (2022).
Rakovszky, T., Sala, P., Verresen, R., Knap, M. & Pollmann, F. Statistical localization: from strong fragmentation to strong edge modes. Phys. Rev. B 101, 125126 https://doi.org/10.1103/PhysRevB.101.125126 (2020).
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 https://doi.org/10.1103/PhysRevB.107.045137 (2023).
Preiss, P. M. et al. Strongly correlated quantum walks in optical lattices. Science 347, 1229 https://doi.org/10.1126/science.1260364 (2015).
Hartmann, T., Keck, F., Korsch, H. J. & Mossmann, S. Dynamics of Bloch oscillations. New J. Phys. 6, 2 https://doi.org/10.1088/1367-2630/6/1/002 (2004).
Movassagh, R. & Shor, P. W. Supercritical entanglement in local systems: counterexample to the area law for quantum matter. Proc. Natl Acad. Sci. USA 113, 13278 https://doi.org/10.1073/pnas.1605716113 (2016).
Movassagh, R. Entanglement and correlation functions of the quantum Motzkin spin-chain. J. Math. Phys. 58, 031901 https://doi.org/10.1063/1.4977829 (2017).
Oh, Y.-T., Han, J. H. & Lee, H.-Y. Fractonic quantum quench in dipole-constrained bosons. Phys. Rev. Res. 6, 023269 https://doi.org/10.1103/PhysRevResearch.6.023269 (2024).
Zhang, S., Lv, C. & Zhou, Q. Synthetic tensor gauge fields. Phys. Rev. Res. 7, 013013 https://doi.org/10.1103/PhysRevResearch.7.013013 (2025).
Wang, Z. & Hazzard, K. R. A. Particle exchange statistics beyond fermions and bosons. Nature 637, 314 https://doi.org/10.1038/s41586-024-08262-7 (2025).
Lukin, A. et al. Probing entanglement in a many-body-localized system. Science 364, 256 https://doi.org/10.1126/science.aau0818 (2019).
Bakr, W. S., Gillen, J. I., Peng, A., Fölling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74 https://doi.org/10.1038/nature08482 (2009).
Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794 https://doi.org/10.1126/science.aaf6725 (2016).
Sidje, R. B. Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Softw. 24, 130–156 https://doi.org/10.1145/285861.285868 (1998).