I am trying to calculate the Pauli limit for a superconducting material with Hamiltonian $H_0$ and an external magnetic field contribution $H_p$. I find the matsubara greens function as $\hat{G} = [i\omega_n - H_0 - H_p]^{-1}$ and then to solve the gap equation for $T_c$ and $H_{c2}$ I calculate the susceptibility as $\chi = \frac{1}{N\beta}\sum_{k,\omega_n} G_{\uparrow\uparrow}(k,i\omega_n)G_{\downarrow\downarrow}(-k,-i\omega_n) - G_{\downarrow\uparrow}(k,i\omega_n)G_{\downarrow\uparrow}(-k,-i\omega_n)$.

I see people here are using specific software and libraries . But I am just using plain python. I generate points in a square BZ with a simple for loop and my problem is the following. When I change the number of points in the grid even slightly the result changes dramatically. How do I properly generate the points in the BZ ? And to perform the summation over k do I need some kind of density of states weighting when I generate the points ? Also the way I am defining the matsubara greens functions the susceptibility is positive. Does this also have to do with the super simple way of generating the points or is my formula incorrect ?



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