Quantum Simulation of the Hubbard Model: Higher Symmetries and New Architectures

The discovery of novel phenomena and phases of matter that are not readily accessible in solid state systems is made possible by the use of ultracold atomic systems as effective instruments for quantum simulation. Experiments with ultracold alkaline-earth-like atoms (AEAs), which exhibit SU(N=2I+1) symmetric interactions, have seen fast improvement in their capabilities. When these atoms are loaded in an optical lattice, they are described by the SU(N) Fermi Hubbard Model (FHM), which is a generalization of the SU(2) FHM and a limit of multiorbital models, both of which are significant in solid state materials such as cuprate and transition metal oxides. According to theoretical calculations, the SU(N) FHM exhibits a wide variety of matter phases, including unusual ones like spin liquids. However, such predictions have been restricted to ground state calculations at one particle per site in the very strong interacting regime. In this talk we reportson the numerical study of the SU(N) FHM at finite temperature, interaction strenghts which span the non-interacting to the strongly interacting limits, as well as different fillings. Results are obtained via a generalized Determinant Quantum Monte Carlo method we developed and are compared against experimental data where possible. The results presented here represent an important step in the understanding of thermodynamic and magnetic properties in the SU(N) FHM and provide tools and guidance for experimental efforts in the field of quantum simulation with AEAs. In the future we expect to further explore and exploit the rich numerical and experimental capabilities to provide a comprehensive study of the phase diagram of the model and elucidate the role played by the enhanced degree of symmetry. An important milestone of the results of this study corresponds to the record temperatures achieved with these quantum simulation architecture: the coldest fermions ever created in nature in absolute temperature and in cold atoms.