Quantum Monte Carlo simulations of superconductivity and magnetism in correlated systems

A hallmark of strongly correlated systems is the emergence of unconventional superconductivity in close proximity to antiferromagnetism. Elucidating the interplay between these two orders, which goes beyond the competition between independent states, remains a major challenge. One of the main hurdles is the difficulty in theoretically accessing the regime of moderate correlations, where the onsite repulsion is comparable to the bandwidth. First, perturbative analytical methods commonly used in the weak-coupling and strong-coupling limits become uncontrolled in this regime. Second, unbiased numerical methods such as Quantum Monte Carlo (QMC) simulations usually suffer from the infamous fermionic sign-problem, except for a very narrow range of parameters (e.g. the half-filled Hubbard model). Interestingly, however, the fermionic sign problem can be circumvented for a much wider range of parameters in certain multi-band electronic models. In this talk, I will present extensive sign-problem-free QMC simulations of two different models: the spin-fermion two-band model and a particular realization of the Hubbard-Kanamori model in a two-band system with dominant inter-band electronic interactions. While in the spin-fermion model the antiferromagnetic fluctuations are preexisting and mediate the pairing interaction between the electrons, in the Hubbard-Kanamori model the same microscopic interactions give rise to both antiferromagnetism and superconductivity. I will compare the phase diagrams of these two models, highlighting the conditions for the emergence of superconductivity and its relationship with magnetic order, charge order, and the metal-to-insulator transition.