The numerical renormalization group (NRG) is a technique devised by Kenneth Wilson to solve certain many-body problems where quantum impurity physics plays a key role.
The numerical renormalization group is an inherently non-perturbative procedure, which was originally used to solve the Kondo model.
The complete behaviour of the Kondo model, including both the high-temperature 'local moment' regime and the low-temperature 'strong coupling' regime are captured by the numerical renormalization group; an exponentially small energy scale TK (not accessible from straight perturbation theory) was shown to govern all properties at low-energies, with all physical observables such as resistivity, thermodynamics, dynamics etc.
In the original example of the Kondo model, the impurity local moment is completely screened below TK by the conduction electrons via the celebrated Kondo effect; and one famous consequence is that such materials exhibit a resistivity minimum at low temperatures, contrary to expectations based purely on the standard phonon contribution, where the resistivity is predicted to decrease monotonically with temperature.
Recent developments[4] make it possible for mapping a general multi-channel conduction-band with channel mixing to a Wilson chain, and here is the python implementation.
This is obviously not the true set of energy levels for the infinite chain, but it is a good approximation to the true set in the temperature range where: the further splittings caused by adding more orbitals is negligible, and we have enough orbitals in the chain to account for splittings which are relevant in this temperature range.
This means that by considering the results at many different chain lengths, one can build up a picture of the behavior of the system over a wide temperature range.