Hidden Bose-Einstein Singularities in Correlated Electron Systems

Abstract

Hidden singularities in correlated electron systems, which are caused by pair fluctuations of electron-electron or electron-hole bubbles obeying Bose-Einstein statistics, are unveiled theoretically. The correlation function of each pair fluctuation is shown to have a bound in the zero Matsubara frequency branch, similarly as the chemical potential of ideal Bose gases. Once the bound is reached, the self-energy starts to acquire a component proportional to Green's function itself, i.e., the structure called one-particle reducible, to keep the correlation function within the bound. The singularities are closely related with, but distinct from, phase transitions with broken symmetries. Passing down through them necessarily accompanies a change in the single-particle density of states around the excitation threshold, such as the pseudo-gap behavior found here for the negative-$U$ Hubbard model above the superconducting transition temperature.