Commit 46e7c347 by Fakher F. Assaad

Editted Readme

1 parent 82981f7d
\begin{eqnarray*}
\hat{\mathcal{H}}&=&\hat{\mathcal{H}}_{T}+\hat{\mathcal{H}}_{V} + \hat{\mathcal{H}}_{I} + \hat{\mathcal{H}}_{0,I}
\end{eqnarray*}
\begin{eqnarray*}
\hat{\mathcal{H}}_{T}
&=&
\sum\limits_{k=1}^{M_T}
\sum\limits_{\sigma=1}^{N_{\mathrm{col}}}
\sum\limits_{s=1}^{N_{\mathrm{fl}}}
\sum\limits_{x,y}^{N_{\mathrm{dim}}}
\hat{c}^{\dagger}_{x \sigma s}T_{xy}^{(k s)} \hat{c}^{\phantom\dagger}_{y \sigma s} \label{eqn:general_ham_t}\\
\hat{\mathcal{H}}_{V}
&=&
\sum\limits_{k=1}^{M_V}U_{k}
\left\{
\sum\limits_{\sigma=1}^{N_{\mathrm{col}}}
\sum\limits_{s=1}^{N_{\mathrm{fl}}}
\left[
\left(
\sum\limits_{x,y}^{N_{\mathrm{dim}}}
\hat{c}^{\dagger}_{x \sigma s}V_{xy}^{(k s)}\hat{c}^{\phantom\dagger}_{y \sigma s}
\right)
+\alpha_{k s}
\right]
\right\}^{2} \label{eqn:general_ham_v}\\
\hat{\mathcal{H}}_{I} & = &
\sum\limits_{k=1}^{M_I} \hat{Z}_{k}
\left(
\sum\limits_{\sigma=1}^{N_{\mathrm{col}}}
\sum\limits_{s=1}^{N_{\mathrm{fl}}}
\sum\limits_{x,y}^{N_{\mathrm{dim}}}
\hat{c}^{\dagger}_{x \sigma s} I_{xy}^{(k s)}\hat{c}^{\phantom\dagger}_{y \sigma s}
\right)
\;.\label{eqn:general_ham_i}
\end{eqnarray*}
# General finite temperature auxiliary field code - ALF release 0.5#
## General information ##
This version of the **A**lgorithms for **L**attice **F**ermions package provides a general code for the finite temperature auxiliary field Quantum Monte Carlo algorithm. The code is engineered to be able simulate any model that can be written in terms of sums of single body operators, of squares of single body operators and single body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the Honeycomb lattice as well as the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation.
This version of the **A**lgorithms for **L**attice **F**ermions package provides a general code for the finite temperature auxiliary field Quantum Monte Carlo algorithm. The code is engineered to be able simulate any model that can be written in terms of sums of single body operators, of squares of single body operators and single body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the Honeycomb lattice as well as the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the [documentation](https://alf.physik.uni-wuerzburg.de/ALF/ALF/raw/master/Documentation/ALF-05.pdf).
The Hamiltonians we can consider read:
![The Hamiltonian0](https://alf.physik.uni-wuerzburg.de/ALF/ALF/raw/master/Images/Hamiltonian0.png)
where
![The Hamiltonian1](https://alf.physik.uni-wuerzburg.de/ALF/ALF/raw/master/Images/Hamiltonian1.png)
Here Z denotes an Ising spin variable with predefined dynamics. If your model can be written in this form then it will be amenable to the ALF.
## PREREQUISITES ##
Libraries: Lapack and Blas
......@@ -25,7 +28,7 @@ Edit **set_env.sh** to provide compiler information and flags as well as loca
**Examples** This directory provides a set of short example runs.
**Documentation** We have included in the file ALF-05.pdf an extensive documentation.
**Documentation** We have included in the file ALF-05.pdf an extensive documentation,
## TESTING ##
......
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