In Fermi liquid theory, the electron spectral function is often represented by $$A(k,\omega) = Z\delta(\omega-\epsilon_k)\ + \text{incoherent background} $$ where $Z$ is the weight in the quasiparticle peak. Consequently, the zero-temperature occupancy $$ n(k)=\int_{-\infty}^0 d\omega A(k,\omega) $$ has a discontinuity of $Z$ at the Fermi level.

However, since the spectral function is actually more accurately described by a Lorentzian with a non-zero width (except right at the Fermi level), is the occupancy, in fact, continuous, and the purported discontinuity only approximate?

This post imported from StackExchange Physics at 2017-02-18 11:09 (UTC), posted by SE-user leongz