Luttinger theorem and nonlinear response of quantum many-particle systems

Abstract

For a general many-electron system, we demonstrate that the Luttinger theorem is obeyed if the electron excitation spectrum is gapless, no matter whether it shows the Landau Fermi liquid or non-Fermi-liquid behavior. Furthermore, we give a general expression of the nonlinear response of the system to external potentials, and apply it for external gauge fields and an on-site time-dependent external potential, where the latter problem can be exactly solved.