Superconductivity in 2D and 3D lattice models of correlated fermions - combining matrix-product states with mean-field theory

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron-pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and unbiased remains a major challenge. Here, we combine matrix-product states (MPS) with static mean field (MF) to provide a solution to this challenge for 2D/3D materials comprised of weakly coupled correlated chains. This framework of Q1D fermions is developed and validated for attractive Hubbard systems and further enhanced via analytical field theory. Finally, we investigate the formation of transient non- quilibrum SC by a real-time evolution of a 3D extended Hubbard system out-of-equilibrium.