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| documentation:language_reference:objects:responsefunction:functions:calculatehybridizationfunction [2024/12/24 00:19] – Maurits W. Haverkort | documentation:language_reference:objects:responsefunction:functions:calculatehybridizationfunction [2025/03/05 15:14] (current) – Maurits W. Haverkort |
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| Responsefunction.CalculateHybridizationFunction(G0,Sigma) calculates the interacting impurity bath Green's function. Given a lattice with local Green's function $G_0(\omega)$ and a local self energy $\Sigma(\omega)$. The full Green's function then is $G(\omega) = G_0(\omega-\Sigma(\omega))$. If we want to add a self energy on all sites, except for the site we are looking at we get $$G_{Bath} = \frac{1}{G_0(\omega-\Sigma(\omega))^{-1} - \Sigma(\omega)}$$ This Green's function can be used to define the hybridisation function of an Anderson impurity model representing a lattice. This is useful for the DMFT approximation where we define a lattice model with local interactions on all lattice sites. We replace the interactions on all sites but one by a local self energy. | Responsefunction.CalculateHybridizationFunction(G0,Sigma) calculates the interacting impurity bath Green's function. Given a lattice with local Green's function $G_0(\omega)$ and a local self energy $\Sigma(\omega)$. The full Green's function then is $G(\omega) = G_0(\omega-\Sigma(\omega))$. If we want to add a self energy on all sites, except for the site we are looking at we get $$G_{Bath} = \frac{1}{G_0(\omega-\Sigma(\omega))^{-1} + \Sigma(\omega)}$$ This Green's function can be used to define the hybridisation function of an Anderson impurity model representing a lattice. This is useful for the DMFT approximation where we define a lattice model with local interactions on all lattice sites. We replace the interactions on all sites but one by a local self energy. |
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