We study a simple electron-phonon model on square and triangular versions of the Lieb lattice using an asymptotically exact strong coupling analysis. At zero temperature and electron density (one electron per unit cell), for various ranges of parameters in the model, we exploit a mapping to the quantum dimer model to establish the existence of a spin-liquid phase with topological order (on the triangular lattice) and a multicritical line corresponding to a quantum critical spin liquid (on the square lattice). In the remaining part of the phase diagram, we find a host of charge-density-wave phases (valence-bond solids), a conventional -wave superconducting phase, and with the addition of a small Hubbard to tip the balance, a phonon-induced -wave superconducting phase. Under a special condition, we find a hidden pseudospin symmetry that implies an exact constraint on the superconducting order parameters.
- Received 2 November 2022
- Accepted 14 April 2023
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Condensed Matter, Materials & Applied Physics