Self Energy

function Fock0_ZeroTemp(q, n, param)

Zero temperature one-spin Fock function for momentum. Assume G0^{-1} = iωn - (k^2/(2m) - E_F) and Yukawa/Coulomb instant interaction.

#Arguments:

• q: momentum
• n: matsubara frequency given in integer s.t. ωn=2πTn
• param: other system parameters

function bandmassratio(param, Σ::GreenFunc.Green2DLR; kamp=param.kF)

calculate the effective band mass of the self-energy at the momentum kamp

\[ \frac{m^*}{m}=z(kamp)^{-1}/\left(1+\frac{Re\Sigma(kamp, 0) - Re\Sigma(0, 0)}{k^2/2m}\right)\]

function massratio(param, Σ::GreenFunc.Green2DLR, δK=5e-6; kamp=param.kF)

calculate the effective mass of the self-energy at the momentum kamp

\[ \frac{m^*_k}{m}=\frac{1}{z_k} \cdot \left(1+\frac{m}{k}\frac{\partial Re\Sigma(k, 0)}{\partial k}\right)^{-1}\]

function zfactor(param, Σ::GreenFunc.Green2DLR; kamp=param.kF, ngrid=[0, 1])

calculate the z-factor of the self-energy at the momentum kamp

\[ z_k=\frac{1}{1-\frac{\partial Im\Sigma(k, 0^+)}{\partial \omega}}\]