lattice/talk-lattice2024
Archived
1
0
Fork 0
Code Activity

incorporate changes discussed on 23.7.

Browse source
This commit is contained in:
Justus Kuhlmann 2024-07-24 14:17:53 +02:00
parent 46774e125b
commit 0d4388b9d7
1 changed files with 22 additions and 13 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

35
talk.tex
View file

@ -35,7 +35,6 @@
\keywords{Münster}
\newcommand{\customcite}[1]{{\color{fu-blue}\citename{#1}{author}}, \citefield{#1}{journaltitle}, {\color{pantone315}\citeyear{#1}}}
\addbibresource{"./My Library.bib"}
\begin{document}
\begin{frame}[plain]
@ -51,7 +50,13 @@
% differences at sym point?
% improvement at the symmetric point
% example
\begin{frame}
\frametitle{What is this all about?}
\begin{itemize}
\item working with exp. Wilson-clover fermions
\item massive $\Rightarrow$ at $N_{\rm f}=3$ symmetric point
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Relevance for further improvement and physics}
\begin{itemize}
@ -72,13 +77,13 @@
\begin{frame}
\frametitle{Determination of $\ca$}
\begin{itemize}
\item Schrödinger functional
\item used already \arxivtag{hep-lat/9609035} for $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
\item from PCAC mass $m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$
\item in Schrödinger functional boundary conditions
\item similar in quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
\item from PCAC mass
\end{itemize}
\vspace{.5cm}
$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}$$
$$\Leftrightarrow \ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$
$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
\end{frame}
\begin{frame}
@ -91,6 +96,9 @@
\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$
\end{itemize}
\item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$ lead to eigenstates $\pi^{(0)}, \pi^{(1)}$
\vspace{.5cm}
\pause
\item project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$
% Question: do we include all wavefunctions or just some?
% How does this interplay with the states that we achieve?
% Which is the optimal wf combination?
@ -112,10 +120,10 @@
$L/a$ & $\beta$ & $\kappa_{1}\approx\kappa_{\rm cr}$ & $\kappa_{2}$ & $\kappa_{3}\approx\kappa_{\rm sym}$&$a$\\
\midrule
24&3.685&0.1396980&0.1395500&0.1394400&0.120\\
32&3.80&0.1392500&---&0.1389630&\\
40&3.90&0.1388562&0.1386148&0.1386030&\\
48&4.00&0.1384942&0.1384880&0.1382720&\\
56&4.10&0.1381410&0.1380000&0.1379450&\\
32&3.80&0.1392500&---&0.1389630&0.095\\
40&3.90&0.1388562&0.1386148&0.1386030&0.080\\
48&4.00&0.1384942&0.1384880&0.1382720&0.064\\
56&4.10&0.1381410&0.1380000&0.1379450&0.055\\
\bottomrule
\end{tabular}
\end{center}
@ -142,10 +150,11 @@
\framesubtitle{Hit symmetric and critical point exactly}
\begin{itemize}
\item ensembles not exactly tuned
\item determine points of interest as in \openlat~ensembles
\item able to interpolate to the desired points due to two or three values per $\beta$
\item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff}
\quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$
\item interpolate to the desired points
\end{itemize}
\end{frame}