Resonating Valence Bond States in an Electron-Phonon System

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Strong Correlation Physics

Background:

• The Lieb lattice is a unique two-dimensional lattice structure exhibiting interesting electronic properties.
• Understanding electron-phonon interactions is crucial for explaining phenomena like superconductivity and charge-density waves.
• Strong coupling regimes often host exotic quantum phases not accessible by conventional methods.

Purpose of the Study:

• To investigate the phase diagram of a simple electron-phonon model on square and triangular Lieb lattices.
• To identify and characterize emergent quantum phases, including spin liquids and superconductors.
• To explore the role of electron-phonon coupling and Hubbard interaction in stabilizing different electronic states.

Main Methods:

• Utilizing an asymptotically exact strong coupling analysis.
• Employing a mapping to the quantum dimer model for analyzing spin-liquid phases.
• Investigating the phase diagram at zero temperature and specific electron densities (n=1).

Main Results:

• Existence of a spin-liquid phase with Z_{2} topological order on the triangular lattice.
• Identification of a multicritical line for a quantum critical spin liquid on the square lattice.
• Discovery of charge-density-wave phases, conventional s-wave superconductivity, and phonon-induced d-wave superconductivity.
• Uncovering a hidden pseudospin SU(2) symmetry with implications for superconducting order parameters.

Conclusions:

• The electron-phonon model on Lieb lattices hosts a rich variety of quantum phases, including topological spin liquids and different superconducting states.
• The interplay between electron-phonon coupling, Hubbard interaction, and lattice geometry dictates the emergent electronic phases.
• The discovered hidden symmetry provides fundamental constraints on the nature of superconductivity in this model.