Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 2012).
Nagaoka, Y. Ferromagnetism in a narrow, almost half-filled s band. Phys. Rev. 147, 392–405 (1966).
Thouless, D. J. Exchange in solid 3He and the Heisenberg Hamiltonian. Proc. Phys. Soc. 86, 893 (1965).
Tasaki, H. Extension of Nagaoka’s theorem on the large-U Hubbard model. Phys. Rev. B 40, 9192–9193 (1989).
Shastry, B. S., Krishnamurthy, H. R. & Anderson, P. W. Instability of the Nagaoka ferromagnetic state of the U = ∞ Hubbard model. Phys. Rev. B 41, 2375–2379 (1990).
White, S. R. & Affleck, I. Density matrix renormalization group analysis of the Nagaoka polaron in the two-dimensional t − J model. Phys. Rev. B 64, 024411 (2001).
Haerter, J. O. & Shastry, B. S. Kinetic antiferromagnetism in the triangular lattice. Phys. Rev. Lett. 95, 087202 (2005).
Anderson, P. W. Resonating valence bonds: a new kind of insulator?. Mater. Res. Bull. 8, 153–160 (1973).
Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).
Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).
Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Doucot, B. & Wen, X. G. Instability of the Nagaoka state with more than one hole. Phys. Rev. B 40, 2719 (1989).
Fang, Y., Ruckenstein, A. E., Dagotto, E. & Schmitt-Rink, S. Holes in the infinite-U Hubbard model: instability of the Nagaoka state. Phys. Rev. B 40, 7406–7409 (1989).
Basile, A. G. & Elser, V. Stability of the ferromagnetic state with respect to a single spin flip: variational calculations for the U = ∞ Hubbard model on the square lattice. Phys. Rev. B 41, 4842–4845 (1990).
Barbieri, A., Riera, J. A. & Young, A. P. Stability of the saturated ferromagnetic state in the one-band Hubbard model. Phys. Rev. B 41, 11697–11700 (1990).
Hanisch, T., Kleine, B., Ritzl, A. & Müller-Hartmann, E. Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular, honeycomb and kagome lattices. Ann. Phys. 507, 303–328 (1995).
Wurth, P., Uhrig, G. & Müller-Hartmann, E. Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state. Ann. Phys. 508, 148–155 (1996).
Park, H., Haule, K., Marianetti, C. A. & Kotliar, G. Dynamical mean-field theory study of Nagaoka ferromagnetism. Phys. Rev. B 77, 035107 (2008).
Liu, L., Yao, H., Berg, E., White, S. R. & Kivelson, S. A. Phases of the infinite U Hubbard model on square lattices. Phys. Rev. Lett. 108, 126406 (2012).
Zhu, Z., Sheng, D. N. & Vishwanath, A. Doped Mott insulators in the triangular-lattice Hubbard model. Phys. Rev. B 105, 205110 (2022).
Dehollain, J. P. et al. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 579, 528–533 (2020).
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).
Ciorciaro, L. et al. Kinetic magnetism in triangular moiré materials. Nature 623, 509–513 (2023).
Xu, M. et al. Frustration- and doping-induced magnetism in a Fermi–Hubbard simulator. Nature 620, 971–976 (2023).
Struck, J. et al. Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996–999 (2011).
Yamamoto, R., Ozawa, H., Nak, D. C., Nakamura, I. & Fukuhara, T. Single-site-resolved imaging of ultracold atoms in a triangular optical lattice. New J. Phys. 22, 123028 (2020).
Yang, J., Liu, L., Mongkolkiattichai, J. & Schauss, P. Site-resolved imaging of ultracold fermions in a triangular-lattice quantum gas microscope. PRX Quantum 2, 020344 (2021).
Mongkolkiattichai, J., Liu, L., Garwood, D., Yang, J. & Schauss, P. Quantum gas microscopy of fermionic triangular-lattice Mott insulators. Phys. Rev. A 108, L061301 (2023).
Trisnadi, J., Zhang, M., Weiss, L. & Chin, C. Design and construction of a quantum matter synthesizer. Rev. Sci. Instrum. 93, 083203 (2022).
Zhang, S.-S., Zhu, W. & Batista, C. D. Pairing from strong repulsion in triangular lattice Hubbard model. Phys. Rev. B 97, 140507 (2018).
van de Kraats, J., Nielsen, K. K. & Bruun, G. M. Holes and magnetic polarons in a triangular lattice antiferromagnet. Phys. Rev. B 106, 235143 (2022).
Davydova, M., Zhang, Y. & Fu, L. Itinerant spin polaron and metallic ferromagnetism in semiconductor moiré superlattices. Phys. Rev. B 107, 224420 (2023).
Chen, S. A., Chen, Q. & Zhu, Z. Proposal for asymmetric photoemission and tunneling spectroscopies in quantum simulators of the triangular-lattice Fermi-Hubbard model. Phys. Rev. B 106, 085138 (2022).
Morera, I., Weitenberg, C., Sengstock, K. & Demler, E. Exploring kinetically induced bound states in triangular lattices with ultracold atoms: spectroscopic approach. Preprint at https://arxiv.org/abs/2312.00768 (2023).
Morera, I. et al. High-temperature kinetic magnetism in triangular lattices. Phys. Rev. Res. 5, L022048 (2023).
Schlömer, H., Schollwöck, U., Bohrdt, A. & Grusdt, F. Kinetic-to-magnetic frustration crossover and linear confinement in the doped triangular t − J model. Preprint at https://arxiv.org/abs/2305.02342 (2023).
Samajdar, R. & Bhatt, R. N. Nagaoka ferromagnetism in doped Hubbard models in optical lattices. Preprint at https://arxiv.org/abs/2305.05683 (2023).
Brinkman, W. F. & Rice, T. M. Single-particle excitations in magnetic insulators. Phys. Rev. B 2, 1324–1338 (1970).
Shraiman, B. I. & Siggia, E. D. Two-particle excitations in antiferromagnetic insulators. Phys. Rev. Lett. 60, 740–743 (1988).
Sachdev, S. Hole motion in a quantum Néel state. Phys. Rev. B 39, 12232–12247 (1989).
Grusdt, F. et al. Parton theory of magnetic polarons: mesonic resonances and signatures in dynamics. Phys. Rev. X 8, 011046 (2018).
Koepsell, J. et al. Imaging magnetic polarons in the doped Fermi–Hubbard model. Nature 572, 358–362 (2019).
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).
Koepsell, J. et al. Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid. Science 374, 82–86 (2021).
Prichard, M. L. et al. Directly imaging spin polarons in a kinetically frustrated Hubbard system. Nature https://doi.org/10.1038/s41586-024-07356-6 (2024).
Yao, H., Tsai, W.-F. & Kivelson, S. A. Myriad phases of the checkerboard Hubbard model. Phys. Rev. B 76, 161104 (2007).
Sposetti, C. N., Bravo, B., Trumper, A. E., Gazza, C. J. & Manuel, L. O. Classical antiferromagnetism in kinetically frustrated electronic models. Phys. Rev. Lett. 112, 187204 (2014).
Kaminski, A. & Das Sarma, S. Polaron percolation in diluted magnetic semiconductors. Phys. Rev. Lett. 88, 247202 (2002).
Szasz, A., Motruk, J., Zaletel, M. P. & Moore, J. E. Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study. Phys. Rev. X 10, 021042 (2020).
Weber, C., Läuchli, A., Mila, F. & Giamarchi, T. Magnetism and superconductivity of strongly correlated electrons on the triangular lattice. Phys. Rev. B 73, 014519 (2006).
Song, X.-Y., Vishwanath, A. & Zhang, Y.-H. Doping the chiral spin liquid: topological superconductor or chiral metal. Phys. Rev. B 103, 165138 (2021).
Morera, I. & Demler, E. Itinerant magnetism and magnetic polarons in the triangular lattice Hubbard model. Preprint at https://arxiv.org/abs/2402.14074 (2024).
Morera, I., Bohrdt, A., Ho, W. W. & Demler, E. Attraction from frustration in ladder systems. Preprint at https://arxiv.org/abs/2106.09600 (2021).
Foutty, B. A. et al. Tunable spin and valley excitations of correlated insulators in γ-valley moiré bands. Nat. Mater. 22, 731–736 (2023).
Tao, Z. et al. Observation of spin polarons in a frustrated moiré Hubbard system. Nat. Phys. https://doi.org/10.1038/s41567-024-02434-y (2024).
Schrieffer, J. R., Wen, X.-G. & Zhang, S.-C. Spin-bag mechanism of high-temperature superconductivity. Phys. Rev. Lett. 60, 944 (1988).
Majumdar, C. K. & Ghosh, D. K. On Next-Nearest-Neighbor Interaction in Linear Chain. I. J. Math. Phys. 10, 1388–1398 (1969).
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, 74–77 (2009).
Parsons, M. F. et al. Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model. Science 353, 1253–1256 (2016).
Khatami, E. & Rigol, M. Thermodynamics of strongly interacting fermions in two-dimensional optical lattices. Phys. Rev. A 84, 053611 (2011).
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).
Zürn, G. et al. Precise characterization of 6Li Feshbach resonances using trap-sideband-resolved RF spectroscopy of weakly bound molecules. Phys. Rev. Lett. 110, 135301 (2013).
Hirthe, S. et al. Magnetically mediated hole pairing in fermionic ladders of ultracold atoms. Nature 613, 463–467 (2023).
Bohrdt, A., Homeier, L., Bloch, I., Demler, E. & Grusdt, F. Strong pairing in mixed-dimensional bilayer antiferromagnetic Mott insulators. Nat. Phys. 18, 651–656 (2022).
Lanczos, C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl Bur. Stand, 45, 255–282 (1950).
Prelovsek, P. in The Physics of Correlated Insulators, Metals, and Superconductors (eds Pavarini, E. et al.) Ch. 7 (Forschungszentrum Jülich, Institute for Advanced Simulation, 2017).
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 (2022).
MacDonald, A. H., Girvin, S. M. & Yoshioka, D. t/U expansion for the Hubbard model. Phys. Rev. B 37, 9753–9756 (1988).
Abrikosov, A. A., Gorkov, L. P. & Dzyaloshnski, I. Y. Methods of Quantum Field Theory in Statistical Physics (Pergamon, 1965).
Rossi, R. Determinant diagrammatic monte carlo algorithm in the thermodynamic limit. Phys. Rev. Lett. 119, 045701 (2017).
Varney, C. N. et al. Quantum monte carlo study of the two-dimensional fermion hubbard model. Phys. Rev. B 80, 075116 (2009).
Rigol, M., Bryant, T. & Singh, R. R. P. Numerical linked-cluster approach to quantum lattice models. Phys. Rev. Lett. 97, 187202 (2006).
Tang, B., Khatami, E. & Rigol, M. A short introduction to numerical linked-cluster expansions. Comp. Phys. Commun. 184, 557–564 (2013).
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).
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