Resonating Valence Bond States in an Electron-Phonon System

Abstract

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 $n=1$ (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 ${\mathbb{Z}}_2$ topological order (on the triangular lattice) and a multi-critical 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 (e.g. valence-bond crystals), a conventional s-wave superconducting phase, and with the addition of a small Hubbard $U$ to tip the balance, a phonon-induced d-wave superconducting phase. Under a special condition, we find a hidden pseudo-spin $SU(2)$ symmetry that implies an exact constraint on the superconducting order parameters.

The title is changed from "Resonating Valence Bond States and other surprises in an Electron-Phonon System"

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Cited by in corpus (11)

• "Quantum bipolaron" superconductivity from quadratic electron-phonon coupling
• Electronic orders on the kagome lattice at the lower Van Hove filling
• Semi-classical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model
• Mixed-state phase transitions in spin-Holstein models
• Emergent Gauge Fields in Band Insulators
• Fractionalization as an alternate to charge ordering in electronic insulators
• Quantum spin liquid from electron-phonon coupling
• Fractionalized Fermi liquids and the cuprate phase diagram
• Models of interacting bosons with exact ground states: a unified approach
• Interplay of frustration and quantum fluctuations in a spin-1/2 anisotropic square lattice
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling