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I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density \begin{equation} \hat{\rho}_{\overrightarrow{q …

As regard the first doubt, From the delta Kronecker we have $$ \vec{k}_1-\vec{k}_4 = \vec{k}_3-\vec{k}_2 $$ so \begin{align*} \vec{q}'&=\vec{k}_1-\vec{k}_4 \\ &=\frac{1}{2}\left(\vec{k}_1 - \vec{k} …

The model that i am studying is the s-f model. I wrote some post about it, then, in order to understund better my notation go to this question Now, I am computing some parameters that emerge out of …

I have to compute the chemical potential in the zero bandwidth s-f model, analized in this article, from the following condition $$ n=\left\langle\hat{n}_{\uparrow}\right\rangle+\left\langle\hat{n}_{ …

I have a doubt on the constraints for the expecation values obtained by Bünemann et all. First i want to introduce my notation To analytically solve a tight-binding model, \begin{equation} \hat{H}= …

The s-f Model is a model who could describe the $\textbf{magnetic 4 $\textit{f}$ systems}$, i.e systems where we could identify localized electrons in $4\,\textit{f}$ orbitals and conductions electro …

I am trying to represent the tight-binding Hamiltonian \begin{equation} \hat{H}_{TB} = \sum_{\sigma} \sum_{\alpha,\beta} \sum_{\mathbf{R}_1,\mathbf{R}_2} t^{\alpha,\beta}_{\mathbf{R}_1,\mathbf{R}_2} …

In (2) we can substitute $t^{\alpha,\beta}_{\mathbf{R}_{1}-\mathbf{R}_{0},\mathbf{R}_{2}-\mathbf{R}_{0}}$. Then since the left hand side of (2) does not depend on $\mathbf{R}_{0}$, if we sum on it w …