loos/CCvsMBPT
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

details in the normal order hamiltonian

Browse Source
This commit is contained in:
Raul QUINTERO MONSEBAIZ 2022-10-13 10:46:52 +02:00
parent 0f3c29f8f4
commit f61dc22754
1 changed files with 3 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
CCvsMBPT.tex
View File

@ -292,7 +292,7 @@ To be more specific, restricting ourselves to CCD, \ie, $\hT = \hT_2$, the eleme
\begin{equation}
\mel*{ \Psi_{i}^{a} }{ \bHN }{ \Psi_{j}^{b} } = \cF_{ab} \delta_{ij} - \cF_{ij} \delta_{ab} + \cW_{jabi}
\end{equation}
where $\bHN = e^{-\hT} \hH e^{\hT} - E_\text{CCD}$ is the normal-ordered similarity-transformed Hamiltonian, $\Psi_{i}^{a}$ are singly-excited determinants, the one-body terms are
where \textcolor{blue}{ $\bHN = e^{-\hT} \hH_{N} e^{\hT} $} is the normal-ordered similarity-transformed Hamiltonian, $\Psi_{i}^{a}$ are singly-excited determinants, the one-body terms are
\begin{subequations}
\begin{align}
\label{eq:cFab}
@ -503,9 +503,9 @@ where $\be{}{\GW}$ is a diagonal matrix collecting the quasiparticle energies, t
\end{subequations}
and the corresponding coupling blocks read
\begin{align}
V^\text{2h1p}_{p,klc} & = \ERI{pc}{kl}
V^\text{2h1p}_{p,klc} & =\textcolor{blue}{\sqrt{2}}\ERI{pc}{kl}
&
V^\text{2p1h}_{p,kcd} & = \ERI{pk}{dc}
V^\text{2p1h}_{p,kcd} & =\textcolor{blue}{\sqrt{2}} \ERI{pk}{dc}
\end{align}
Going beyond the Tamm-Dancoff approximation is possible, but more cumbersome. \cite{Bintrim_2021}