Bottom-up configuration-interaction emulations of ultracold fermions in entangled optical plaquettes: building blocks of unconventional superconductivity

A microscopic configuration-interaction (CI) methodology is introduced to enable bottom-up Schrödinger-equation emulation of unconventional superconductivity in ultracold optical traps. We illustrate the method by exploring the properties of Li atoms in a single square plaquette in the hole-pairing regime, and by analyzing the entanglement (symmetry-preserving) and disentanglement physics (via symmetry-breaking, associated with the separation of charge and spin density waves) of two coupled plaquettes in the same regime. The single-occupancy RVB states contribute only partially to the exact many-body solutions, and the CI results map onto a Hubbard Hamiltonian, but not onto the double-occupancy-excluding t-J one. For the double-plaquette case, effects brought about by breaking the symmetry between two weakly-interacting plaquettes, either by distorting, or by tilting and detuning, one of the plaquettes with respect to the other, as well as spectral changes caused by increased coupling between the two plaquettes, are explored.