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The propagation is set through the call: +The data in the \verb|Hopping_matrix_type| type suffices to uniquely define the unit step propagation for the kinetic energy, and for any combinations of the \texttt{Checkerboard} and \texttt{Symm} options (see Sec.~\ref{sec:trotter}). The propagation is set through the call: \begin{lstlisting}[style=fortran] Call Predefined_Hoppings_set_OPT(Hopping_Matrix, List, Invlist, Latt, Latt_unit, Dtau, Checkerboard, Symm, OP_T, pinned_vertices, pinning_factor, pinning_offset) \end{lstlisting} -in which the operator array \path{OP_T(*,N_FL)} is allocated and defined. In the simplest case, where no checkerboard is used, the array's first dimension is unity. This routine allows optional -arguments to allow for pinning: that is, modifying existing matrix elements in the hopping matrix. The syntax is the following: +in which the operator array \verb|OP_T(*,N_FL)| is allocated and defined. In the simplest case, where no checkerboard is used, the array's first dimension is unity. + +This routine allows optional arguments to allow for pinning: that is, modifying existing matrix elements in the hopping matrix. The syntax is the following: \begin{itemize} -\item \texttt{pinned\_vertices[1:N\_pin,1:2]} contains the two legs $(i,\delta)$ and $(j,\delta')$ of the bond or vertex to be pinned. If $(i,\delta) = (j,\delta')$ then the pinning refers to a site and not to a bond. -\item \texttt{pinning\_factor[1:N\_pin,1:N\_fl]} contains the multiplicative factor for each flavor. -\item \texttt{pinning\_offset[1:N\_pin,1:N\_fl]} contains the offset for each flavor. +\item \verb|pinned_vertices[1:N_pin, 1:2]| contains the index of the two legs \verb|pinned_vertices[i, 1]| and \verb|pinned_vertices[i, 2]| of the i-th vertex to be pinned, where \verb|N_pin| is the number of pinned vertices. If \verb|pinned_vertices[i, 1]| = \verb|pinned_vertices[i, 2]| then the pinning refers to a site and not to a bond. +\item \verb|pinning_factor[1:N_pin, 1:N_fl]| contains the multiplicative factor for each flavor. Meaning that the matrix element gets multiplied by this factor. +\item \verb|pinning_offset[1:N_pin, 1:N_fl]| contains the offset for each flavor. Meaning that this value gets added to the matrix element after multiplication by the pinning factor. \end{itemize} An explicit example of how to use the pinning option is describe in Sec.~\ref{sec:hubbard}. -The data in the \texttt{Hopping\_matrix\_type} type equally suffices to compute the kinetic energy. This is carried out in the routine \texttt{Predefined\_Hoppings\_Compute\_Kin}. +The data in the \verb|Hopping_matrix_type| type equally suffices to compute the kinetic energy. This is carried out in the routine \verb|Predefined_Hoppings_Compute_Kin|. \subsubsection{An example: nearest neighbor hopping on the honeycomb lattice }