Magnetic properties of materials ranging from conventional ferromagnetic metals to strongly correlated materials such as cuprates originate from Coulomb exchange interactions. The existence of alternate mechanisms for magnetism that could naturally facilitate electrical control has been discussed theoretically^1–7, but an experimental demonstration⁸ in an extended system has been missing. Here we investigate MoSe₂/WS₂ van der Waals heterostructures in the vicinity of Mott insulator states of electrons forming a frustrated triangular lattice and observe direct evidence of magnetic correlations originating from a kinetic mechanism. By directly measuring electronic magnetization through the strength of the polarization-selective attractive polaron resonance^9,10, we find that when the Mott state is electron-doped, the system exhibits ferromagnetic correlations in agreement with the Nagaoka mechanism.

We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intraspecies interactions provided they are balanced by comparable attractive interspecies interactions. The ground-state phase diagram is presented and the different phases are characterized by examining the density profile and off-diagonal one- and two-body correlation functions. A rich variety of phases is found, including atomic superfluid gases, atomic superfluid droplets, pair superfluid droplets, pair superfluid gases, and a Mott-insulator phase. A parameter region prone to be experimentally explored is identified, where the average population per site is lower than three atoms, thus avoiding three-body losses. Finally, the bipartite entanglement of the droplets is found to have a nontrivial dependence on the number of particles.

We study kinetic magnetism for the Fermi-Hubbard model in triangular lattices. We focus on the regime of strong interactions, $U\gg t$, and filling factors around one electron per site. For temperatures well above the hopping strength $t$, the Curie-Weiss form of the magnetic susceptibility suggests two complementary forms of kinetic magnetism. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes, whereas for electron doping, Nagaoka-type ferromagnetic correlations are induced by propagating doublons. These results provide a possible theoretical explanation of recent experimental results in moiré transition metaldichalcogenide materials and cold atom systems. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole-doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields, we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field, the system shows a tendency to phase separate with hole-rich regions forming antiferromagnetic spin bags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.

We study the properties of a single impurity in a dilute Bose gas, a Bose polaron, using the functional renormalization group. We use an ansatz for the effective action motivated by a derivative expansion, and we compute the energies of the attractive and repulsive branches of excitations in both two and three spatial dimensions. Three-body correlations play an important role in the attractive branch, and we account for those by including three-body couplings between two bath bosons and the impurity. Our calculations compare very favorably with state-of-the-art experimental measurements and numerical simulations.