Motivated by the pseudogap state of the cuprates, we introduce the concept of an “exceptional” van Hove singularity that appears when a strong electron-electron interaction splits an otherwise simply connected Fermi surface into multiply connected pieces. The singularity describes the touching of two pieces of the split Fermi surface. We show that this singularity is proximate to a second-order van Hove singularity, which can be accessed by tuning a dispersion parameter. We argue that, in a wide class of cuprates, the endpoint of the pseudogap is accessed only by triggering the exceptional van Hove singularity. The resulting Lifshitz transition is characterized by enhanced specific heat and nematic susceptibility, as seen in experiments.

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• Density of states
• Pseudogap
• Superconducting gap
• Superconducting phase transition
• 2-dimensional systems
• Cuprates
• High-temperature superconductors
• Strongly correlated systems
• Green's function methods
• Non-Fermi-liquid theory
• Quantum field theory