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 ${}^6\mathrm{Li}$ 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 resonating valence bond 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.

• Received 9 December 2016
• Revised 30 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.043617