If site 0 is in the central region

Assume that

$$\Sigma_R(\omega ^-) = \omega _0 /2 + i \Gamma _0/2$$ (231)

where $\omega ^\pm=\omega \pm i \delta$.

$$G_C = (\omega - \Sigma_R - \Sigma_L)$$ (232)

$$\Sigma_R(\omega ^-) = {\rm Re }\Sigma_R+ i {\rm Im }\Sigma_R = \omega _0 /2 + i \Gamma _0/2$$ (233)

$$\Sigma_R(\omega ^+) = {\rm Re }\Sigma_R- i {\rm Im }\Sigma_R = \omega _0 /2 - i \Gamma _0/2$$ (234)

$$\Gamma = {\rm Im} (\Sigma_R(\omega ^-) - \Sigma_R(\omega ^+)) = \Gamma _0$$ (235)

Then

$$G_C(\omega ^+) = 1/( \omega - \omega _0 - i \Gamma _0 )$$ (236)

conductance is

$$T = \Gamma G_C(\omega ^+) \Gamma G_C(\omega ^-)$$ (237)

$$= \Gamma _0^2 / ( (\omega - \omega _0)^2 + \Gamma _0^2)$$ (238)

where $\omega _0$ and $\Gamma _0$ are functions of $\omega$ and must be calculated. $\omega _0=\omega$ in the range from $-2t$ to $2t$ also from numerical calculations. Therefore $T=1$ from $\omega =-2t$ to $\omega =2t$, and $G_C= 1/(-i \Gamma _0)$.