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We study quantum oscillations for a system of fermionic and bosonic dimersand compare the results to those experimentally observed in the cupratesuperconductors in their underdoped regime. Based on gauge invariance, we arguethat the charge carriers obey the Onsager quantization condition and quantumoscillations take on a Lifshitz-Kosevich form. We obtain the effective mass andfind good qualitative agreement with experiments if we tune the model to thepoint where the observed mass divergence at optimum doping is associated to avan Hove singularity at which four free-dimer Fermi pockets touch pairwise inthe interior of the Brillouin zone. The same van Hove singularity leads to amaximum in the d-wave superconducting pairing amplitude when anti-ferromagneticinteractions are included. Our combined results therefore suggest that aquantum critical point separating the underdoped and overdoped regimes ismarked by the location of the van Hove saddle point in the fermionic dimerdispersion.

Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates