The numerical renormalization group method for quantum impurity systems

TL;DR

This paper reviews the numerical renormalization group (NRG) method, a non-perturbative technique developed in the 1970s for solving quantum impurity problems, highlighting its applications over 30 years.

Contribution

It provides an overview of the NRG method, including calculation guidelines and a survey of its development and diverse applications in quantum impurity systems.

Findings

Successfully characterized the crossover in the Kondo problem.

Extended NRG to non-Fermi liquid behaviors and dissipative systems.

Applied NRG within dynamical mean field theory for lattice systems.

Abstract

In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG has been later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method including some guidelines of how to calculate physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean field theory.