loos/SRGGW
2
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

saving work

Browse Source
This commit is contained in:
Pierre-Francois Loos 2023-03-10 10:16:56 +01:00
parent 4da8ebd479
commit 7786071c6c
1 changed files with 2 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
Manuscript/SRGGW.tex
View File

@ -302,8 +302,8 @@ where $\boldsymbol{\eta}(s)$, the flow generator, is defined as
\begin{equation} \begin{equation}
\boldsymbol{\eta}(s) = \dv{\bU(s)}{s} \bU^\dag(s) = - \boldsymbol{\eta}^\dag(s). \boldsymbol{\eta}(s) = \dv{\bU(s)}{s} \bU^\dag(s) = - \boldsymbol{\eta}^\dag(s).
\end{equation} \end{equation}
The flow equation can then be approximately solved by introducing an approximate form of $\boldsymbol{\eta}(s)$.
The flow equation can be approximately solved by introducing an approximate form of $\boldsymbol{\eta}(s)$.
In this work, we consider Wegner's canonical generator \cite{Wegner_1994} In this work, we consider Wegner's canonical generator \cite{Wegner_1994}
\begin{equation} \begin{equation}
\boldsymbol{\eta}^\text{W}(s) = \comm{\bH^\text{d}(s)}{\bH(s)} = \comm{\bH^\text{d}(s)}{\bH^\text{od}(s)}, \boldsymbol{\eta}^\text{W}(s) = \comm{\bH^\text{d}(s)}{\bH(s)} = \comm{\bH^\text{d}(s)}{\bH^\text{od}(s)},
@ -414,7 +414,7 @@ Therefore, it is natural to define, within the SRG formalism, the diagonal and o
\end{align} \end{align}
\end{subequations} \end{subequations}
where we omit the $s$ dependence of the matrices for the sake of brevity. where we omit the $s$ dependence of the matrices for the sake of brevity.
Then, the aim is to solve, order by order, the flow equation \eqref{eq:flowEquation} knowing that the initial conditions are Then, our aim is to solve, order by order, the flow equation \eqref{eq:flowEquation} knowing that the initial conditions are
\begin{subequations} \begin{subequations}
\begin{align} \begin{align}
\bHd{0}(0) & = \mqty( \bF & \bO \\ \bO & \bC ), \bHd{0}(0) & = \mqty( \bF & \bO \\ \bO & \bC ),