@@ -220,7 +220,7 @@ For Windows and other Linuxes and Unixes, please check the Tutorials' repository
\section*{Starting}
Jupyter notebooks\footnote{Note that pyALF can also be used to start a simulation from the command line, without starting a Jupyter server or using a notebook. For instance: \texttt{python3.7 Run.py -R --alfdir /home/debian/ALF-1.2/--config "Intel" --executable\_R Hubbard --mpi True} starts a parallel run of the Hubbard model, using ALF compiled with \texttt{ifort}. Notice that \texttt{Run.py} requires a configuration file \texttt{Sims}, which defines the simulation parameters. An entry of \texttt{Sims} might read as: \texttt{{"Model": "Hubbard", "Lattice\_type": "Square", "L1": 4, "L2": 4, "NBin": 5, "ham\_T": 0.0, "Nsweep" : 2000, "Beta": 1.0, "ham\_chem": -1.0}}}\href{https://jupyter.readthedocs.io/en/latest/running.html}{are run} through a Jupyter server started, e.g., from the command line:
Jupyter notebooks\href{https://jupyter.readthedocs.io/en/latest/running.html}{are run} through a Jupyter server\footnote{Note that pyALF can also be used to start a simulation from the command line, without starting a Jupyter server or using a notebook. For instance: \texttt{python3.7 Run.py -R --alfdir /home/debian/ALF-1.2/--config "Intel" --executable\_R Hubbard --mpi True} starts a parallel run of the Hubbard model, using ALF compiled with \texttt{ifort}. Notice that \texttt{Run.py} requires a configuration file \texttt{Sims}, which defines the simulation parameters. An entry of \texttt{Sims} might read as: \texttt{{"Model": "Hubbard", "Lattice\_type": "Square", "L1": 4, "L2": 4, "NBin": 5, "ham\_T": 0.0, "Nsweep" : 2000, "Beta": 1.0, "ham\_chem": -1.0}}} started, e.g., from the command line:
\begin{lstlisting}[style=bash]
jupyter notebook
\end{lstlisting}
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@@ -265,15 +265,16 @@ which opens the ``notebook dashboard'' in your default browser, where you can na
\part{Getting your hands dirty - writing new code}
%\setcounter{exercise}{0}
This second part of the tutorial consists in a set of guided advanced exercises.
A lot already comes implemented in ALF, but unavoidably, as one proceeds in their own investigations, a new model has to be implemented or a new observable defined -- and for that, one must grapple with the package's Fortran source code.
This second part of the tutorial consists in a set of guided exercises that exemplify how to make basic additions to the code, taking as starting point the template-like, relatively self-contained module \texttt{Hamiltonian\_Hubbard\_Plain\_Vanilla\_mod.F90}, which is also a good display of ALF's internal workings.
A lot already comes implemented in ALF, but unavoidably, as one proceeds in their own investigations, a new model has to be implemented or a new observable defined -- and for that one has to grapple with the package's Fortran source code. However, in ALF this is made easy by means of predefined structures, templates, and the examples below.
These worked-out exercises, together with ALF's modularity provided by its Predefined Structures should make getting your hands dirty less daunting than it may sound.
\section*{Downloading the code and tutorial}
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@@ -281,7 +282,9 @@ One can use the ALF package downloaded automatically by the Python script in the
in a shell. And to download the tutorial, including solutions:
in a shell. The necessary environment variables and the directives for compiling the code are set by the script \texttt{configure.sh}: \lstinline[style=bash]|source configure.sh GNU|, followed by the command \lstinline[style=bash,morekeywords={make}]|make|. Details and further options are described in the package's documentation found in its repository.
Similarly, to download the tutorial, including solutions, enter:
Here we will modify the code so as to allow for different hopping matrix elements along the x and y directions of a square lattice. To do so, one merely has to do the following
Here we will modify the code so as to allow for different hopping matrix elements along the $x$ and $y$ directions of a square lattice. To do so we start from the module \texttt{Hamiltonian\_Hubbard\_Plain\_Vanilla\_mod.F90} found in \texttt{<ALF\_DIR>/Prog/Hamiltonians/}, which we will simply call ``\texttt{Vanilla}'', and then:
\begin{itemize}
\item Add an extra variable, \texttt{Ham\_Ty}, in the parameter file in the \texttt{VAR\_Hubbard} name space
\item Declare the variable \texttt{Ham\_Ty} in the \texttt{Hamiltonian\_Examples.f90}.
\item Read in this variable in \texttt{Ham\_set} subroutine of the \texttt{Hamiltonian\_Examples.f90} file.
\item Modify the hopping matrix in the subroutine \texttt{Ham\_Hop} in the \texttt{Hamiltonian\_Examples.f90} file.
\item Declare a new variable, \texttt{Ham\_Ty}, in the module's specification (just search for the declaration of \texttt{Ham\_T} in \texttt{Vanilla}).
\item Add \texttt{Ham\_Ty} to the \texttt{VAR\_Hubbard\_Plain\_Vanilla} name space in the parameter file \texttt{parameters}.
\item Add this variable also to the name space (\texttt{namelist}) declaration at the \texttt{Ham\_Set} subroutine of \texttt{Vanilla}.
\item Modify the hopping matrix in the subroutine \texttt{Ham\_Hop} in \texttt{Vanilla}:
Op_T(1,nf)%O(Iy, I ) = cmplx(-Ham_Ty, 0.d0, kind(0.D0))
!!!!!!!
endif
Op_T(1,nf)%O(I, I ) = cmplx(-Ham_chem, 0.d0, kind(0.D0))
Op_T(1,nf)%P(i) = i
Enddo
\end{lstlisting}
\end{itemize}
In the directory \texttt{Solutions/Exercise\_2} we have duplicated the ALF and commented the changes that have to be carried out to the file
\texttt{Hamiltonian\_Examples.f90} in the \texttt{Prog} directory.
Note: If you'd like to run the simulation using MPI, you should also add the broadcasting call for \texttt{Ham\_Ty} to \texttt{Ham\_Set}.
\red{[NOT yet done. Necessary?]} In the directory \texttt{Solutions/Exercise\_2} we have duplicated the ALF and commented the changes that have to be carried out to the file \texttt{Hamiltonian\_Hubbard\_Plain\_Vanilla\_mod.F90} in the \texttt{Prog} directory.
\noindent
As an application of this code, one can consider a ladder system, defined by the parameter file:
! slash terminates namelist statement - DO NOT REMOVE
\end{lstlisting}
As an application of this code, one can consider a 2-leg ladder system defined, e.g., with \texttt{L1=14}, \texttt{L2=2}, \texttt{Lattice\_type="Square"}, \texttt{Model="Hubbard\_Plain\_Vanilla"} and \texttt{Ham\_Ty=2.0D0}.
% [Excluding the introduction to the exercise item: improved estimator \langle \vec{S}_{i} \cdot \vec{S}_{j} \rangle]
The SU(2) Hubbard-Stratonovich decomposition, conserves spin rotational symmetry. Run the ladder code with the SU(2) flag in the parameter file switched on (i.e. \texttt{Model = Hubbard\_SU2}) and compare results.
\red{[HOW to best implement this? Introduce modifications to \texttt{Hamiltonian\_Hubbard\_mod.F90}?]}The SU(2) Hubbard-Stratonovich decomposition, conserves spin rotational symmetry. Run the ladder code with the SU(2) flag in the parameter file switched on (i.e. \texttt{Model = Hubbard\_SU2}) and compare results.
