Modeling unconventional superconductivity at the crossover between strong and weak electronic interactions

The interplay between superconductivity and magnetism in correlated systems is an outstanding question in condensed matter physics. It has been recently shown that the two-band spin-fermion model, in which electrons interact with pre-existing magnetic fluctuations, can be simulated by Quantum Monte Carlo (QMC) without the fermionic sign-problem. Here we go beyond this approach and present sign-problem-free QMC results of a two-band microscopic model in which both superconductivity and magnetism arise from the very same inter-band repulsion, without pre-existing bosons mediating the electronic interactions. Our simulations reveal the interplay between a host of different phenomena as the interaction strength is increased. A wide magnetic dome appears at moderate values of the interaction, whereas a narrow superconducting dome emerges around the magnetic quantum critical point located on the less strongly correlated side of the phase diagram. Interestingly, a metal-insulator transition is nearly coincident with this magnetic phase boundary, and is manifested by a change in the magnetic dynamics from overdamped to propagating. The emergence of superconductivity only in the former region provides important clues about the nature of the pairing glue in unconventional superconductors.