Commit 49127767 authored by Jefferson Stafusa E. Portela's avatar Jefferson Stafusa E. Portela
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Correct typos; minor.

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......@@ -99,7 +99,7 @@ Percent_change = 0.1 ! Parameter P
/
\end{lstlisting}
By setting $\alpha$ to zero we can test this code against the Hubbard code. For a $ 4 \times 4 $ square lattice at $ \beta t = 5$, $U/t = 4$, and half-band filling, \texttt{Hamiltonian\_Hubbard\_mod.F90} gives $ E = -13.1889 \pm 0.0017 $ and \texttt{Hamiltonian\_LRC\_mod.F90}, $E = -13.199 \pm 0.040 $. Note that for the Hubbard code we have used the default \texttt{Mz = .True.}. This option breaks SU(2) spin symmetry for a given HS configuration, but produces very precise values of the energy. On the other hand, the LRC code is an SU(2) invariant code (as would be choosing \texttt{Mz = .False.}) and produces more fluctuations in the double occupancy. This partly explains the difference in error bars between the two codes. To produce this data, one can run the pyALF python script \href{https://git.physik.uni-wuerzburg.de/ALF/pyALF/-/blob/\pyALFbranch/Scripts/LRC.py}{\texttt{LRC.py}}.
By setting $\alpha$ to zero we can test this code against the Hubbard code. For a $ 4 \times 4 $ square lattice at $ \beta t = 5$, $U/t = 4$, and half-band filling, \texttt{Hamiltonian\_Hubbard\_smod.F90} gives $ E = -13.1889 \pm 0.0017 $ and \texttt{Hamiltonian\_LRC\_smod.F90}, $E = -13.199 \pm 0.040 $. Note that for the Hubbard code we have used the default \texttt{Mz = .True.}. This option breaks SU(2) spin symmetry for a given HS configuration, but produces very precise values of the energy. On the other hand, the LRC code is an SU(2) invariant code (as would be choosing \texttt{Mz = .False.}) and produces more fluctuations in the double occupancy. This partly explains the difference in error bars between the two codes. To produce this data, one can run the pyALF python script \href{https://git.physik.uni-wuerzburg.de/ALF/pyALF/-/blob/\pyALFbranch/Scripts/LRC.py}{\texttt{LRC.py}}.
% The definition of the Coulomb repulsion is as follows.
%A general lattice site \texttt{I,n} where \texttt{I: 1...Latt\%N} is the unit cell and \texttt{ n = 1 ...Latt\_unit\%NORB} the orbital is given by:
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% !TEX root = doc.tex
%{\color{red} We have to restructure this section. As it stands it is a chaos. We have to separate more clearly data structures, specification of the model, and the Input output. }
%\red{Also mention:}\\
%Also available is the \texttt{Hopping\_Matrix\_type}, defined in Sec.~\ref{sec:hopping_type}, used for defining hopping matrices.
......@@ -144,7 +143,7 @@ For such auxiliary fields a dedicated type \texttt{Fields} is defined, whose com
%------------------------------------------------------------
ALF's lattice module can generate one- and two-dimensional Bravais lattices.
Both the lattice and the unit cell are defined in the module \texttt{Lattices\_v3\_mod.F90} and their components are detailed in Tables \ref{table:lattice} and \ref{table:unit_cell}.
Both the lattice and the unit cell are defined in the module \texttt{lattices\_v3\_mod.F90} and their components are detailed in Tables \ref{table:lattice} and \ref{table:unit_cell}.
As its name suggest the module \texttt{Predefined\_Latt\_mod.F90} also provides predefined lattices as described in Sec.~\ref{sec:predefined_lattices}.
The user who wishes to define his/her own lattice has to specify: 1) unit vectors $\vec{a}_1$ and $\vec{a}_2$, 2) the size and shape of the lattice, characterized by the vectors $\vec{L}_1$ and $\vec{L}_2$ and 3) the unit cell characterized be the number of orbitals and their positions. The coordination number of the lattice is specified in the \texttt{Unit\_cell} data type. The lattice is placed on a torus (periodic boundary conditions):
\begin{equation}
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......@@ -195,7 +195,6 @@ A short review on various computational approaches to quantum entanglement in in
ALF provides predefined observables to compute the second R\'enyi entropy and its associated mutual information, see Sec.~\ref{sec:renyi}.
% Removed to refer to predefined obs. instead: In the subroutines \path{Obser} and \path{ObserT} of the module \path{Hamiltonian_Examples_mod.F90} (see Sec.~\ref{sec:obs}) the user is provided with
In Sec.~\ref{sec:predefined_observales} we describe the equal-time and time-displaced correlation functions that come predefined in ALF.
Using the above formulation of Wick's theorem, arbitrary correlation functions can be computed (see Appendix \ref{Wick_appendix}). We note, however, that the program is limited to the calculation of observables that contain only two different imaginary times.
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