Typical medium dynamical cluster approximation: Difference between revisions

Revision as of 00:51, 7 June 2024

Revision as of 00:56, 7 June 2024

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<math>\rho_t^c(\mathbf{K}, \omega) = \left\langle \rho^c_i\right\rangle_\mathrm{geom} \left\langle \frac{\rho^c(\mathbf{K})}{\frac{1}{N_c} \sum_{i}\rho_i^c}\right\rangle_\mathrm{arit}</math>

Here, <math>\left\langle \rho^c_i\right\rangle_\mathrm{geom} = \exp\left(\left\langle \ln\rho_i\right\rangle_\mathrm{arit}\right)</math> is the geometric mean of the diagonal elements of the density of states, capturing non-local fluctuations.

4. Calculate the cluster typical Green’s function <math>G_t^c(\mathbf{K})</math> from the [[Kramers–Kronig relations|Kramers Kronig transform]] of the density of states, used to compute the coarse-grained Green’s function:

<math>\bar{G}(\mathbf{K}) = \frac{N_c}{N} \sum_{\tilde{k}} \left[\left(G^c_t(\mathbf{K})^{-1} + \Gamma(\mathbf{K}) - H_0(k) + \bar{H}_0(\mathbf{K}) + \mu\right)^{-1}\right]</math>

where <math>\mu</math> is the Fermi level obtained in the secondary SCF loop.

5. Obtain a new hybridization function based on a mixture of old and updated functions, with the linear mixing parameter <math>\zeta</math>: