Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Bohrdt, A., Homeier, L., Reinmoser, C., Demler, E. & Grusdt, F. Exploration of doped quantum magnets with ultracold atoms. Ann. Phys. 435, 168651 (2021).
Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1994).
Carroll, A. N. et al. Observation of generalized t–J spin dynamics with tunable dipolar interactions. Science 388, 381–386 (2025).
Gorshkov, A. V. et al. Tunable superfluidity and quantum magnetism with ultracold polar molecules. Phys. Rev. Lett. 107, 115301 (2011).
Qin, M. et al. Absence of superconductivity in the pure two-dimensional Hubbard model. Phys. Rev. X 10, 031016 (2020).
Jiang, H.-C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t′. Science 365, 1424–1428 (2019).
Jiang, Y.-F., Devereaux, T. P. & Jiang, H.-C. Ground-state phase diagram and superconductivity of the doped Hubbard model on six-leg square cylinders. Phys. Rev. B 109, 085121 (2024).
Xu, H. et al. Coexistence of superconductivity with partially filled stripes in the Hubbard model. Science 384, eadh7691 (2024).
Bespalova, T. A., Delić, K., Pupillo, G., Tacchino, F. & Tavernelli, I. Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer. Phys. Rev. A 111, 052619 (2025).
Bohrdt, A. et al. Microscopy of bosonic charge carriers in staggered magnetic fields. Preprint at https://arxiv.org/abs/2410.19500 (2024).
Homeier, L. et al. Antiferromagnetic bosonic t–J models and their quantum simulation in tweezer arrays. Phys. Rev. Lett. 132, 230401 (2024).
Browaeys, A. & Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132–142 (2020).
Mögerle, J. et al. Spin-1 haldane phase in a chain of Rydberg atoms. PRX Quantum 6, 020332 (2025).
Liu, V. S. et al. Supersolidity and simplex phases in spin-1 Rydberg atom arrays. Preprint at https://arxiv.org/abs/2407.17554 (2024).
Scalapino, D. J. A common thread: the pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 1383–1417 (2012).
Proust, C. & Taillefer, L. The remarkable underlying ground states of cuprate superconductors. Annu. Rev. Condens. Matter Phys. 10, 409–429 (2019).
Bednorz, J. G. & Müller, K. A. Possible highTc superconductivity in the Ba–La–Cu–O system. Z. Phys. B Condensed Matter 64, 189–193 (1986).
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).
Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).
Shao, H.-J. et al. Antiferromagnetic phase transition in a 3D fermionic Hubbard model. Nature 632, 267–272 (2024).
Hirthe, S. et al. Magnetically mediated hole pairing in fermionic ladders of ultracold atoms. Nature 613, 463–467 (2023).
Lebrat, M. et al. Observation of Nagaoka polarons in a Fermi–Hubbard quantum simulator. Nature 629, 317–322 (2024).
Prichard, M. L. et al. Directly imaging spin polarons in a kinetically frustrated Hubbard system. Nature 629, 323–328 (2024).
Duan, L.-M., Demler, E. & Lukin, M. D. Controlling spin exchange interactions of ultracold atoms in optical lattices. Phys. Rev. Lett. 91, 090402 (2003).
Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).
Emery, V. J., Kivelson, S. A. & Lin, H. Q. Phase separation in the t–J model. Phys. Rev. Lett. 64, 475 (1990).
Boninsegni, M. Phase separation in mixtures of hard core bosons. Phys. Rev. Lett. 87, 087201 (2001).
Sun, H. et al. Realization of a bosonic antiferromagnet. Nat. Phys. 17, 990–994 (2021).
Jepsen, P. N. et al. Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms. Phys. Rev. X 11, 041054 (2021).
Harris, T. J., Schollwöck, U., Bohrdt, A. & Grusdt, F. Kinetic magnetism and stripe order in the doped AFM bosonic t–J model. Preprint at https://arxiv.org/abs/2410.00904v1 (2024).
Zhang, H.-K., Zhang, J.-X., Xu, J.-S. & Weng, Z.-Y. Quantum-interference-induced pairing in antiferromagnetic bosonic t–J model. Preprint at https://arxiv.org/abs/2409.15424 (2024).
Siller, T., Troyer, M., Rice, T. M. & White, S. R. Bosonic model of hole pairs. Phys. Rev. B 63, 195106 (2001).
O’Mahony, S. M. et al. On the electron pairing mechanism of copper-oxide high temperature superconductivity. Proc. Natl. Acad. Sci. 119, e2207449119 (2022).
Morera, I., Bohrdt, A., Ho, W. W. & Demler, E. Attraction from kinetic frustration in ladder systems. Phys. Rev. Res. 6, 023196 (2024).
Sous, J. & Pretko, M. Fractons from polarons. Phys. Rev. B 102, 214437 (2020).
Barredo, D. et al. Coherent excitation transfer in a spin chain of three Rydberg atoms. Phys. Rev. Lett. 114, 113002 (2015).
Emperauger, G. et al. Benchmarking direct and indirect dipolar spin-exchange interactions between two Rydberg atoms. Phys. Rev. A 111, 062806 (2025).
Wadenpfuhl, K. & Adams, C. S. Unravelling the structures in the van der Waals interactions of alkali Rydberg atoms. Phys. Rev. A 111, 062803 (2025).
Winkler, K. et al. Repulsively bound atom pairs in an optical lattice. Nature 441, 853–856 (2006).
Staszewski, L. & Wietek, A. Quench dynamics of stripes and phase separation in the two-dimensional t–J model. Phys. Rev. B 112, 035125 (2025).
White, S. R. & Scalapino, D. J. Phase separation and stripe formation in the two-dimensional t–J model: a comparison of numerical results. Phys. Rev. B 61, 6320 (2000).
Kagan, M. Y., Kugel, K. I. & Rakhmanov, A. L. Electronic phase separation: recent progress in the old problem. Phys. Rep. 916, 1–105 (2021).
Ji, G. et al. Coupling a mobile hole to an antiferromagnetic spin background: transient dynamics of a magnetic polaron. Phys. Rev. X 11, 021022 (2021).
Chen, C. et al. Continuous symmetry breaking in a two-dimensional Rydberg array. Nature 616, 691–695 (2023).
Weber, S. et al. Tutorial: Calculation of Rydberg interaction potentials. J. Phys. B: At. Mol. Opt. Phys. 50, 133001 (2017).
Marder, M., Papanicolaou, N. & Psaltakis, G. C. Phase separation in a t–J model. Phys. Rev. B 41, 6920 (1990).
Bobroff, J. et al. Absence of static phase separation in the high Tc cuprate YBa2Cu3O6+y. Phys. Rev. Lett. 89, 157002 (2002).
Daley, A. J. Quantum trajectories and open many-body quantum systems. Adv. Phys. 63, 77–149 (2014).
Hauschild, J. et al. Tensor network Python. Code available at https://github.com/tenpy/tenpy/. Documentation available at https://tenpy.readthedocs.io/en/latest/ (2018).
Hauschild, J. & Pollmann, F. Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy). SciPost Phys. Lect. Notes https://doi.org/10.21468/scipostphyslectnotes.5 (2018).