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

TL;DR

This paper uses sign-problem-free Quantum Monte Carlo methods to study a multi-band Hubbard model, revealing how antiferromagnetism, metal-insulator crossover, and superconductivity interrelate in intermediate electronic interaction regimes.

Contribution

It introduces a sign-problem-free multi-band Hubbard model that captures the interplay of superconductivity, magnetism, and charge correlations without fine-tuning.

Findings

Antiferromagnetic order forms a dome in the intermediate-coupling regime.

Superconductivity appears near the antiferromagnetic quantum phase transition.

Magnetic fluctuations change character across the quantum phase transition.

Abstract

High-temperature superconductivity emerges in a host of different quantum materials, often in a region of the phase diagram where the electronic kinetic energy is comparable in magnitude with the electron-electron Coulomb repulsion. Describing such an intermediate-coupling regime has proven challenging, as standard perturbative approaches are inapplicable. Hence, it is of enormous interest to find models that are amenable to be solved using exact methods. While important advances have been made in elucidating the properties of one such minimal model -- the Hubbard model -- via numerical simulations, the infamous fermionic sign-problem significantly limits the accessible parameter space. Here, we employ Quantum Monte Carlo (QMC) methods to solve a multi-band version of the Hubbard model that does not suffer from the sign-problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free QMC studies, this model does not have pre-existing fine-tuned magnetic order, and thus treats superconducting, magnetic, and charge degrees of freedom on an equal footing. We find that, as the electron-electron repulsion increases, a dome of antiferromagnetic order emerges in the intermediate-coupling regime, accompanied by a metal-to-insulator crossover line. Superconductivity is found only near the antiferromagnetic quantum phase transition located on the metallic side of the magnetic dome. Across the antiferromagnetic quantum phase transition we find a change in the dynamical character of the magnetic fluctuations, from slow and overdamped in the metallic side to fast and propagating in the insulating side. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.