nrgplusplus#
Efficient Numerical Renormalization Group (NRG) calculations in Modern C++
nrgplusplus is a high-performance C++ library for solving quantum impurity problems
using the Numerical Renormalization Group method. It is designed for studying strongly
correlated electron systems including:
Kondo effect and quantum impurities
Single Impurity Anderson Model (SIAM)
Multi-channel and multi-impurity systems
Magnetic impurities in superconductors, Yu-Shiba-Rusinov states
The library provides a modular, template-based architecture that is both flexible for model development and optimized for computational speed using Intel MKL.
Architecture Overview#
Core Components:
nrgcore: Main NRG solver class that manages iterations
Impurity models: Define the quantum impurity (e.g., Anderson model, Kondo model)
Bath models: Define the environment or conduction band
Symmetries: Block-diagonalize by conserved quantum numbers (charge, spin, etc.)
Every impurity or bath model must provide:
std::vector<qOperator> f_dag_operator— Fermionic creation operators
std::vector<std::vector<double>> eigenvalues_Q— Eigenvalues per quantum number sector
std::vector<double> chi_Q— Fermion signs (parity)
std::vector<std::vector<int>> n_Q— Quantum numbers labeling each sector
Quick Start Example: Single Impurity Anderson Model (SIAM)#
Reference: Bulla et al., Rev. Mod. Phys. 80, 395 (2008)
1. Define the impurity and bath models:
// Impurity: single orbital with onsite energy and Hubbard U
spinhalf impurity(eps=-1.0, U_int=2.0);
// Bath: non-interacting conduction electrons
spinhalf bathModel(eps=0, U_int=0);
2. Create the NRG solver and configure:
nrgcore<spinhalf, spinhalf> siam(impurity, bathModel);
siam.set_parameters(1024); // Keep up to 1024 states per iteration
3. Run NRG iterations:
h5stream::h5stream results("siam_output.h5"); // Save results to HDF5
double Lambda = 2.0; // RG flow parameter
for (int iteration = 0; iteration < nMax; iteration++) {
double V = 0.5; // Impurity-bath coupling
double rescale = (iteration > 0) ? std::sqrt(Lambda) : 1.0;
siam.add_bath_site({V, V}, rescale);
siam.update_internal_state();
results.write(siam.all_eigenvalue, "iteration" + std::to_string(iteration));
}
results.close();
4. Visualize results:
Plot RG flow (see examples/rgflowSIAM/plot.py)
