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Fermi gases and liquids display an excitation spectrum that is simplyconnected, ensuring closed Fermi surfaces. In strongly correlated systems likethe cuprate superconductors, the existence of open sheets of Fermi surfaceknown as Fermi arcs indicates a distinctly different topology of the spectrumwith no equivalent in Fermi liquid theory. Here, we demonstrate a genericmechanism by which correlation effects in fermionic systems can change thetopology of the spectrum. Using diagrammatic Monte Carlo simulations, wedemonstrate the existence of disconnected and multiply connected excitationspectra in the attractive Hubbard model in the BCS-BEC cross-over regime. Thesetopologically nontrivial spectra are a prerequisite for Fermi arcs.

Disconnected and multiply connected spectra in the 2D attractive Hubbard model