### Merge branch 'master' of https://alf.physik.uni-wuerzburg.de/ALF/ALF-Tutorial

 ... ... @@ -108,6 +108,9 @@ %--------------------------------------------------------------------------------------------------------- \maketitle \section*{Downloading the code and tutorial} To download the code, type \texttt{ git clone https://alf.physik.uni\-wuerzburg.de/ALF/ALF.git } in a shell. \\ To download the tutorial including solutions type: \\ \texttt{git clone https://alf.physik.uni-wuerzburg.de/ALF/ALF-Tutorial.git} again in a shell. \section*{Exercise 1) Testing against ED} Run the code with the Mz choice of Hubbard Stratonovitch transformation on a four site ring, at $U/t=4$ and inverse temperature $\beta t = 2$. For this set of parameters, the exact internal energy reads: ... ... @@ -197,7 +200,7 @@ Here we will modify the code so as to allow for different hopping matrix eleme \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\_Latt} in the \texttt{Hamiltonian\_Examples.f90 } file. \item Modify the hopping matrix in the subroutine \texttt{Ham\_Hop} in the \texttt{Hamiltonian\_Examples.f90 } file. \lstset{style=fortran} \begin{lstlisting} DO I = 1, Latt%N ... ... @@ -216,7 +219,7 @@ ENDDO \end{lstlisting} \end{itemize} In the directory \texttt{Exercise\_2/solutions} we have duplicated the ALF and commented the changes that have to be carried out to the file 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. ... ... @@ -312,7 +315,7 @@ The above form is readily included in the ALF since the interaction is written H = -t \sum_{i} \left( c^{\dagger}_{i} c^{\phantom\dagger}_{i+a} + c^{\dagger}_{i+a} c^{\phantom\dagger}_{i} \right) + V \sum_{i} \left( n_{i} - 1/2 \right) \left( n_{i+a} - 1/2 \right) \end{equation} In the directory \texttt{Exercise\_3/solutions} we have duplicated the ALF and commented the changes that have to be carried out to the file In the directory \texttt{Solutions/Exercise\_3} 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 so as to include the t$\_$V model. Here are the steps to be carried out. \begin{itemize} ... ...
 ******************************************************************************* Mon Jan 29 09:16:21 2018 FIT: data read from "Ener.dat" u (($1)*($1)):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:23:40 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:24:19 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:25:09 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:25:36 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:26:18 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:26:32 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:27:00 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:27:23 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Mon Jan 29 10:27:50 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Thu Feb 1 05:48:24 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1 After 6 iterations the fit converged. final sum of squares of residuals : 0.697788 rel. change during last iteration : -6.19392e-11 degrees of freedom (FIT_NDF) : 1 rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 0.835337 variance of residuals (reduced chisquare) = WSSR/ndf : 0.697788 Final set of parameters Asymptotic Standard Error ======================= ========================== a = -1.47328 +/- 0.001698 (0.1153%) b = -5.00419 +/- 0.1405 (2.808%) correlation matrix of the fit parameters: a b a 1.000 b -0.913 1.000 ******************************************************************************* Thu Feb 1 05:48:43 2018 FIT: data read from "Ener.dat" u ($1*$1):2:3 format = x:z:s #datapoints = 3 function used for fitting: f(x) fitted parameters initialized with current variable values Iteration 0 WSSR : 9.33551e+06 delta(WSSR)/WSSR : 0 delta(WSSR) : 0 limit for stopping : 1e-05 lambda : 491.183 initial set of free parameter values a = 1 b = 1