Spin correlations and thermometry in the SU(2) and SU(N) Hubbard model

Cold atom quantum simulators of the 2D Fermi-Hubbard model and its SU(N)-symmetric extension have provided key insights into the low-temperature and strongly correlated regions of its phase diagram, surpassing numerical methods. However, these experiments require comparison with precise numerical for thermometry. The spin correlation function for nearest and next-nearest neighbours has been shown to saturate with decreasing temperature, making it unsuitable as a thermometer in the ultra-low-temperature regime. We instead explore thermometry with the momentum-space spin correlation function using unbiased diagrammatic Monte Carlo with the Combinatorial Summation (CoS) algorithm, which scales independently of spin flavour number, to study its dependence on interaction strength, temperature, doping, and number of spins.