Nontrivial saddle points for spectral form factors of flat band superconductors

Abstract We derive the spectral form factor of a flat band superconductor in two different ways. In the first approach, we diagonalize the Hamiltonian of this system exactly and numerically sum over the exact eigenstates to find the spectral form factor. In the second approach, we use mean field theory to evaluate the same spectral form factor. We demonstrate that both methods produce the same answer. Mean field theory for spectral form factors possesses features not previously seen in the theory of superconductivity, in particular complex gap functions and non-Hermitian effective Hamiltonians. We explicitly show that these features are indeed necessary to obtain the correct spectral form factor.