We provide a quantitative and controlled analysis of the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model on a lattice, in the normal and superconducting states. We analyze the entire crossover from Bardeen-Cooper-Schrieffer (BCS)/weak coupling to Eliashberg/strong coupling superconductivity, as a function of fermion-boson interaction strength and hopping parameter. Cooper pairs of sharp Fermi-liquid quasiparticles at weak coupling evolve into pairing of fully incoherent fermions in the non-Fermi liquid regime. The crossovers leave observable traces in the critical temperature, the zero-temperature and zero-energy gap, the entropy, and the phase stiffness.

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• Bosons
• Electron-phonon coupling
• Fermions
• Meissner effect
• Optical & microwave phenomena
• Pairing mechanisms
• Spin-singlet pairing
• Superconducting gap
• Superconducting order parameter
• Superconducting phase transition
• Superfluid density
• BCS theory
• Conformal field theory
• Eliashberg theory
• Exact solutions for many-body systems
• Large-N expansion in field theory
• Mean field theory
• Non-Fermi-liquid theory
• Sachdev-Ye-Kitaev model