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Pierre-Francois Loos 2023-03-10 10:16:56 +01:00
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Manuscript/SRGGW.tex
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@ -302,8 +302,8 @@ where $\boldsymbol{\eta}(s)$, the flow generator, is defined as
\begin{equation}
\boldsymbol{\eta}(s) = \dv{\bU(s)}{s} \bU^\dag(s) = - \boldsymbol{\eta}^\dag(s).
\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}
\begin{equation}
\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{subequations}
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{align}
\bHd{0}(0) & = \mqty( \bF & \bO \\ \bO & \bC ),