Commit 5326bf4f authored by Jefferson Stafusa E. Portela's avatar Jefferson Stafusa E. Portela
Browse files

New projective question; remark on beta version of ALF 2.0.

parent f67db5b9
...@@ -173,7 +173,7 @@ The ALF package provides a general code for auxiliary-field Quantum Monte Carlo ...@@ -173,7 +173,7 @@ The ALF package provides a general code for auxiliary-field Quantum Monte Carlo
\item[Part II.] The second part is independent of the first and aimed at more advanced users who want to simulate their own systems. It guides the user on how to modify the package's Fortran source code and presents the resources implemented to facilitate this task. \item[Part II.] The second part is independent of the first and aimed at more advanced users who want to simulate their own systems. It guides the user on how to modify the package's Fortran source code and presents the resources implemented to facilitate this task.
\end{description} \end{description}
This document is intended to be self-contained, but the interested reader should check \href{https://git.physik.uni-wuerzburg.de/ALF/ALF/-/blob/master/Documentation/doc.pdf}{ALF's documentation}, which contains a thorough, systematic description of the package. This document is intended to be self-contained, but the interested reader should check \href{https://git.physik.uni-wuerzburg.de/ALF/ALF/-/blob/master/Documentation/doc.pdf}{ALF's documentation}, which contains a thorough, systematic description of the package in its 2.0 (beta) version.
% Old link: \href{https://git.physik.uni-wuerzburg.de/ALF/ALF_code/blob/master/Documentation/ALF_v1.0.pdf}{ALF's documentation} % Old link: \href{https://git.physik.uni-wuerzburg.de/ALF/ALF_code/blob/master/Documentation/ALF_v1.0.pdf}{ALF's documentation}
......
...@@ -27,7 +27,7 @@ further details, see Sec. 3 of ...@@ -27,7 +27,7 @@ further details, see Sec. 3 of
\href{https://git.physik.uni-wuerzburg.de/ALF/ALF_code/-/blob/master/Documentation/ALF_v1.0.pdf}{ALF \href{https://git.physik.uni-wuerzburg.de/ALF/ALF_code/-/blob/master/Documentation/ALF_v1.0.pdf}{ALF
documentation}. documentation}.
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} \begin{center}\rule{0.5\linewidth}{\linethickness}\end{center}
\textbf{1.} Import \texttt{Simulation} class from the \texttt{py\_alf} \textbf{1.} Import \texttt{Simulation} class from the \texttt{py\_alf}
python module, which provides the interface with ALF, as well as python module, which provides the interface with ALF, as well as
...@@ -36,10 +36,10 @@ numerical and plotting packages: ...@@ -36,10 +36,10 @@ numerical and plotting packages:
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{1}{\boxspacing} \prompt{In}{incolor}{1}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}] \begin{Verbatim}[commandchars=\\\{\}]
\PY{k+kn}{from} \PY{n+nn}{py\PYZus{}alf} \PY{k+kn}{import} \PY{n}{Simulation} \PY{c+c1}{\PYZsh{} Interface with ALF} \PY{k+kn}{from} \PY{n+nn}{py\PYZus{}alf} \PY{k}{import} \PY{n}{Simulation} \PY{c+c1}{\PYZsh{} Interface with ALF}
\PY{c+c1}{\PYZsh{} } \PY{c+c1}{\PYZsh{} }
\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} \PY{c+c1}{\PYZsh{} Numerical library} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} \PY{c+c1}{\PYZsh{} Numerical library}
\PY{k+kn}{from} \PY{n+nn}{scipy}\PY{n+nn}{.}\PY{n+nn}{optimize} \PY{k+kn}{import} \PY{n}{curve\PYZus{}fit} \PY{c+c1}{\PYZsh{} Numerical library} \PY{k+kn}{from} \PY{n+nn}{scipy}\PY{n+nn}{.}\PY{n+nn}{optimize} \PY{k}{import} \PY{n}{curve\PYZus{}fit} \PY{c+c1}{\PYZsh{} Numerical library}
\PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} \PY{c+c1}{\PYZsh{} Plotting library} \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} \PY{c+c1}{\PYZsh{} Plotting library}
\end{Verbatim} \end{Verbatim}
\end{tcolorbox} \end{tcolorbox}
...@@ -137,14 +137,14 @@ Run /home/stafusa/Programs/ALF/Prog/Hubbard.out ...@@ -137,14 +137,14 @@ Run /home/stafusa/Programs/ALF/Prog/Hubbard.out
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{6}{\boxspacing} \prompt{In}{incolor}{6}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}] \begin{Verbatim}[commandchars=\\\{\}]
\PY{o}{\PYZpc{}\PYZpc{}capture} \PY{o}{\PYZpc{}\PYZpc{}}\PY{k}{capture}
\PY{n}{ener} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{sims}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} \PY{c+c1}{\PYZsh{} Matrix for storing energy values} ener = np.empty((len(sims), 2)) \PYZsh{} Matrix for storing energy values
\PY{n}{thetas} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{sims}\PY{p}{)}\PY{p}{,}\PY{p}{)}\PY{p}{)} \PY{c+c1}{\PYZsh{} Matrix for Thetas values, for plotting} thetas = np.empty((len(sims),)) \PYZsh{} Matrix for Thetas values, for plotting
\PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{sim} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{sims}\PY{p}{)}\PY{p}{:} for i, sim in enumerate(sims):
\PY{n+nb}{print}\PY{p}{(}\PY{n}{sim}\PY{o}{.}\PY{n}{sim\PYZus{}dir}\PY{p}{)} \PY{c+c1}{\PYZsh{} Directory containing the simulation output} print(sim.sim\PYZus{}dir) \PYZsh{} Directory containing the simulation output
\PY{n}{sim}\PY{o}{.}\PY{n}{analysis}\PY{p}{(}\PY{p}{)} \PY{c+c1}{\PYZsh{} Perform default analysis} sim.analysis() \PYZsh{} Perform default analysis
\PY{n}{thetas}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{sim}\PY{o}{.}\PY{n}{sim\PYZus{}dict}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Theta}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{c+c1}{\PYZsh{} Store Theta value} thetas[i] = sim.sim\PYZus{}dict[\PYZsq{}Theta\PYZsq{}] \PYZsh{} Store Theta value
\PY{n}{ener}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{sim}\PY{o}{.}\PY{n}{get\PYZus{}obs}\PY{p}{(}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Ener\PYZus{}scalJ}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Ener\PYZus{}scalJ}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{obs}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{c+c1}{\PYZsh{} Store internal energy} ener[i] = sim.get\PYZus{}obs([\PYZsq{}Ener\PYZus{}scalJ\PYZsq{}])[\PYZsq{}Ener\PYZus{}scalJ\PYZsq{}][\PYZsq{}obs\PYZsq{}] \PYZsh{} Store internal energy
\end{Verbatim} \end{Verbatim}
\end{tcolorbox} \end{tcolorbox}
...@@ -185,7 +185,7 @@ For Theta values [ 5. 10. 20.] the measured energies are: ...@@ -185,7 +185,7 @@ For Theta values [ 5. 10. 20.] the measured energies are:
\end{center} \end{center}
{ \hspace*{\fill} \\} { \hspace*{\fill} \\}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} \begin{center}\rule{0.5\linewidth}{\linethickness}\end{center}
\hypertarget{exercises}{% \hypertarget{exercises}{%
\subsection{Exercises}\label{exercises}} \subsection{Exercises}\label{exercises}}
...@@ -194,10 +194,16 @@ For Theta values [ 5. 10. 20.] the measured energies are: ...@@ -194,10 +194,16 @@ For Theta values [ 5. 10. 20.] the measured energies are:
\def\labelenumi{\arabic{enumi}.} \def\labelenumi{\arabic{enumi}.}
\tightlist \tightlist
\item \item
\textbf{{[} TO BE FLESHED OUT {]}} Kondo phase transition. A ladder system consists of chains assembled one next to the other,
References:\\ for instance, setting \texttt{L1=14}, \texttt{L2=3} defines a 3-leg
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.63.155114\\ ladder. It is a well-known result
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.83.796 {[}\href{doi.org/10.1126/science.271.5249.618}{Dagotto and Rice,
\emph{Science} 271 (1996), \textbf{5249}, pp.~618}{]} that spin
correlations in ladder systems decay as power laws (apart from
logarithmic corrections) for odd-leg ladders, and exponentially for
even-leg ladders. The paper presents numerical results for the
Heisenberg model. How do these correlations behave for the Hubbard
model at half-filling?
\end{enumerate} \end{enumerate}
......
...@@ -395,7 +395,7 @@ further details, see Sec. 3 of ...@@ -395,7 +395,7 @@ further details, see Sec. 3 of
\href{https://git.physik.uni-wuerzburg.de/ALF/ALF_code/-/blob/master/Documentation/ALF_v1.0.pdf}{ALF \href{https://git.physik.uni-wuerzburg.de/ALF/ALF_code/-/blob/master/Documentation/ALF_v1.0.pdf}{ALF
documentation}. documentation}.
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} \begin{center}\rule{0.5\linewidth}{\linethickness}\end{center}
\textbf{1.} Import \texttt{Simulation} class from the \texttt{py\_alf} \textbf{1.} Import \texttt{Simulation} class from the \texttt{py\_alf}
python module, which provides the interface with ALF, as well as python module, which provides the interface with ALF, as well as
...@@ -404,10 +404,10 @@ numerical and plotting packages: ...@@ -404,10 +404,10 @@ numerical and plotting packages:
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{1}{\boxspacing} \prompt{In}{incolor}{1}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}] \begin{Verbatim}[commandchars=\\\{\}]
\PY{k+kn}{from} \PY{n+nn}{py\PYZus{}alf} \PY{k+kn}{import} \PY{n}{Simulation} \PY{c+c1}{\PYZsh{} Interface with ALF} \PY{k+kn}{from} \PY{n+nn}{py\PYZus{}alf} \PY{k}{import} \PY{n}{Simulation} \PY{c+c1}{\PYZsh{} Interface with ALF}
\PY{c+c1}{\PYZsh{} } \PY{c+c1}{\PYZsh{} }
\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} \PY{c+c1}{\PYZsh{} Numerical library} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} \PY{c+c1}{\PYZsh{} Numerical library}
\PY{k+kn}{from} \PY{n+nn}{scipy}\PY{n+nn}{.}\PY{n+nn}{optimize} \PY{k+kn}{import} \PY{n}{curve\PYZus{}fit} \PY{c+c1}{\PYZsh{} Numerical library} \PY{k+kn}{from} \PY{n+nn}{scipy}\PY{n+nn}{.}\PY{n+nn}{optimize} \PY{k}{import} \PY{n}{curve\PYZus{}fit} \PY{c+c1}{\PYZsh{} Numerical library}
\PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} \PY{c+c1}{\PYZsh{} Plotting library} \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} \PY{c+c1}{\PYZsh{} Plotting library}
\end{Verbatim} \end{Verbatim}
\end{tcolorbox} \end{tcolorbox}
...@@ -505,14 +505,14 @@ Run /home/stafusa/Programs/ALF/Prog/Hubbard.out ...@@ -505,14 +505,14 @@ Run /home/stafusa/Programs/ALF/Prog/Hubbard.out
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder] \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{6}{\boxspacing} \prompt{In}{incolor}{6}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}] \begin{Verbatim}[commandchars=\\\{\}]
\PY{o}{\PYZpc{}\PYZpc{}capture} \PY{o}{\PYZpc{}\PYZpc{}}\PY{k}{capture}
\PY{n}{ener} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{sims}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} \PY{c+c1}{\PYZsh{} Matrix for storing energy values} ener = np.empty((len(sims), 2)) \PYZsh{} Matrix for storing energy values
\PY{n}{thetas} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{sims}\PY{p}{)}\PY{p}{,}\PY{p}{)}\PY{p}{)} \PY{c+c1}{\PYZsh{} Matrix for Thetas values, for plotting} thetas = np.empty((len(sims),)) \PYZsh{} Matrix for Thetas values, for plotting
\PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{sim} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{sims}\PY{p}{)}\PY{p}{:} for i, sim in enumerate(sims):
\PY{n+nb}{print}\PY{p}{(}\PY{n}{sim}\PY{o}{.}\PY{n}{sim\PYZus{}dir}\PY{p}{)} \PY{c+c1}{\PYZsh{} Directory containing the simulation output} print(sim.sim\PYZus{}dir) \PYZsh{} Directory containing the simulation output
\PY{n}{sim}\PY{o}{.}\PY{n}{analysis}\PY{p}{(}\PY{p}{)} \PY{c+c1}{\PYZsh{} Perform default analysis} sim.analysis() \PYZsh{} Perform default analysis
\PY{n}{thetas}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{sim}\PY{o}{.}\PY{n}{sim\PYZus{}dict}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Theta}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{c+c1}{\PYZsh{} Store Theta value} thetas[i] = sim.sim\PYZus{}dict[\PYZsq{}Theta\PYZsq{}] \PYZsh{} Store Theta value
\PY{n}{ener}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{sim}\PY{o}{.}\PY{n}{get\PYZus{}obs}\PY{p}{(}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Ener\PYZus{}scalJ}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Ener\PYZus{}scalJ}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{obs}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{c+c1}{\PYZsh{} Store internal energy} ener[i] = sim.get\PYZus{}obs([\PYZsq{}Ener\PYZus{}scalJ\PYZsq{}])[\PYZsq{}Ener\PYZus{}scalJ\PYZsq{}][\PYZsq{}obs\PYZsq{}] \PYZsh{} Store internal energy
\end{Verbatim} \end{Verbatim}
\end{tcolorbox} \end{tcolorbox}
...@@ -553,7 +553,7 @@ For Theta values [ 5. 10. 20.] the measured energies are: ...@@ -553,7 +553,7 @@ For Theta values [ 5. 10. 20.] the measured energies are:
\end{center} \end{center}
{ \hspace*{\fill} \\} { \hspace*{\fill} \\}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} \begin{center}\rule{0.5\linewidth}{\linethickness}\end{center}
\hypertarget{exercises}{% \hypertarget{exercises}{%
\subsection{Exercises}\label{exercises}} \subsection{Exercises}\label{exercises}}
...@@ -562,10 +562,16 @@ For Theta values [ 5. 10. 20.] the measured energies are: ...@@ -562,10 +562,16 @@ For Theta values [ 5. 10. 20.] the measured energies are:
\def\labelenumi{\arabic{enumi}.} \def\labelenumi{\arabic{enumi}.}
\tightlist \tightlist
\item \item
\textbf{{[} TO BE FLESHED OUT {]}} Kondo phase transition. A ladder system consists of chains assembled one next to the other,
References:\\ for instance, setting \texttt{L1=14}, \texttt{L2=3} defines a 3-leg
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.63.155114\\ ladder. It is a well-known result
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.83.796 {[}\href{doi.org/10.1126/science.271.5249.618}{Dagotto and Rice,
\emph{Science} 271 (1996), \textbf{5249}, pp.~618}{]} that spin
correlations in ladder systems decay as power laws (apart from
logarithmic corrections) for odd-leg ladders, and exponentially for
even-leg ladders. The paper presents numerical results for the
Heisenberg model. How do these correlations behave for the Hubbard
model at half-filling?
\end{enumerate} \end{enumerate}
......
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