nrgplusplus

nrgplusplus is a modern C++ implementation of the Numerical Renormalization Group (NRG) method, designed to solve quantum impurity problems embedded in a bath. This implementation adheres to the conventions outlined in Bulla, 2008.

Documentation

Comprehensive documentation is available at:
https://srbhp.github.io/nrgplusplus/

Quick Start Guide

For a quick setup and build instructions, refer to:
https://srbhp.github.io/nrgplusplus/build.html

Example: Single Impurity Anderson Model (SIAM)

(See: examples/rgflowSIAM/main.cpp)

Define the impurity model with onsite energy eps and Coulomb energy U_int:

spinhalf impurity(eps, U_int);

The bath for the SIAM is constructed similarly:

spinhalf bathModel(0, 0); // set parameters

Once the impurity and bath are defined, construct an nrgcore object to handle 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 between the impurity and the first bath site
siam.update_internal_state();

Next, iteratively add bath sites and save eigenvalues to an HDF5 file:

// File where output will be written
h5stream::h5stream rfile("resultSIAM.h5");

// Iteratively 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 here if needed before updating the internal state
  siam.update_internal_state();
  // Save the eigenvalues 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):

Contributing

Contributions are welcome! For major changes, please open an issue first to discuss your ideas.
Ensure that tests are updated as appropriate.

Similar Open-source Projects

1. http://www.phy.bme.hu/~dmnrg/
2. https://github.com/rokzitko/nrgljubljana

Acknowledgment

This project was developed with the support of:

• Prof. Jonas Fransson, Uppsala University
• Prof. Frithjof Anders, Technical University Dortmund

Their guidance and support were instrumental in making this project possible.