nrgplusplus

This is a modern C++ implementation of the Numerical Renormalization Group (NRG) Method to solve Quantum Impurity problems embeded in a Bath. We tried to follow the convention of Bulla, 2008.

Documentation

https://srbhp.github.io/nrgplusplus/

Quick Start Guide

https://srbhp.github.io/nrgplusplus/build.html

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).

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Similar Open-source Projects

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

Acknowledgment

During the development of this project I was employed by

• Prof. Jonas Fansson, Uppsala University and
• Prof. Frithjof Anders, Technical University Dortmund.

This project would have been not possible without their support.