nrgplusplus#
The numerical renormalization group (NRG) method is a powerful technique for investigating the low-energy properties of strongly correlated electronic systems. It has found widespread applications in condensed matter physics, including the study of quantum impurity models and the Kondo effect. In order to facilitate the implementation of the NRG method, several software packages have been developed, each with its own strengths and limitations.
nrgplusplus is implementation of the NRG method is written in the Modern C++ programming language. This package provides a versatile and efficient framework for performing NRG calculations. The C++ language is well-suited to numerical calculations, and the package has been designed with efficiency and speed in mind.
nrgcore takes two class as a template argument
for the Impurity model and the bath model. The bath model
is a class that describes bath. The impurity model is a class
that describes the impurity. In some cases the impurity class
model is also include the first Wilson site.
Each Model (bath or impurity) class should have these member vairables:
std::vector<qOperator> f_dag_operator
std::vector<std::vector<double>> eigenvalues_Q
std::vector<double> chi_Q
std::vector<std::vector<int>> n_Q
Example : Single Impurity Anderson Impurity (SIAM)#
(See : examples/rgflowSIAM/main.cpp)
Define the impurity Model wth onsite energy eps and Coulomb energy U_int.
spinhalf impurity(eps, U_int);
The bath for the SIAM is also constructed in the same way.
spinhalf bathModel(0, 0); // set parameters
Once we have created the bath and the impurity we can construct a nrgcore object which will take care of many things that we need to do for the NRG iterations. This includes calculating static and dynamic quantities of the Impurity.
nrgcore<spinhalf, spinhalf> siam(impurity, bathModel);
siam.set_parameters(1024); // set max number of states to be kept
siam.add_bath_site({V, V}, 1.0); // V is the coupling og the impurity and first bath site.
siam.update_internal_state();
Next we iteratively add the bath sites in the same way. We also create HDF5 file object to save the Eigenvalues.
// file where outputput will be wriiten
h5stream::h5stream rfile("resultSIAM.h5");
// Iterative add bath sites
for (int in = 0; in < nMax; in++) {
double rescale = 1.0;
if (in > 0) {
rescale = std::sqrt(LAMBDA);
}
siam.add_bath_site({hopping(in, LAMBDA), hopping(in, LAMBDA)}, rescale);
// Update System Operators now here if we need to.
// This has to be done before updating the systems internal state.
siam.update_internal_state();
// Save the eigenvalue of the current iteration
rfile.write(siam.all_eigenvalue, "Eigenvalues" + std::to_string(in));
}
rfile.close();
Plot the RG flow (See : examples/rgflowSIAM/plot.py).
