The numerical renormalization group method for quantum impurity systems

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.Comment: 55 pages, 27 figures, submitted to Rev. Mod. Phy

Modulated Kondo screening along magnetic mirror twin boundaries in monolayer MoS2 on graphene

A many-body resonance emerges at the Fermi energy when an electron bath screens the magnetic moment of a half-filled impurity level. This Kondo effect, originally introduced to explain the abnormal resistivity behavior in bulk magnetic alloys, has been realized in many quantum systems over the past decades, such as quantum dots, quantum point contacts, nanowires, single-molecule transistors, heavy-fermion lattices, down to adsorbed single atoms. Here we describe a unique Kondo system which allows us to experimentally resolve the spectral function consisting of impurity levels and Kondo resonance in a large Kondo temperature range, as well as their spatial modulation. Our experimental Kondo system, based on a discrete half-filled quantum confined state within a MoS2 grain boundary, in conjunction with numerical renormalization group calculations, enables us to test the predictive power of the Anderson model which is the basis of the microscopic understanding of Kondo physics

Magnetic-Field Universality of the Kondo Effect Revealed by Thermocurrent Spectroscopy

Probing the universal low-temperature magnetic-field scaling of Kondo-correlated quantum dots via electrical conductance has proved to be experimentally challenging. Here, we show how to probe this in nonlinear thermocurrent spectroscopy applied to a molecular quantum dot in the Kondo regime. Our results demonstrate that the bias-dependent thermocurrent is a sensitive probe of universal Kondo physics, directly measures the splitting of the Kondo resonance in a magnetic field, and opens up possibilities for investigating nanosystems far from thermal and electrical equilibrium.QN/van der Zant La

Data supplementary to the publication: Magnetic-Field Universality of the Kondo Effect Revealed by Thermocurrent Spectroscopy

The experimental data and theoretical simulation for " Magnetic-Field Universality of the Kondo Effect Revealed by Thermocurrent Spectroscopy" published on Physical Review Letters.  In this letter, we show the universality in the Kondo effect via the thermocurrent spectroscopy. It is now a new hallmark for the Kondo effect in thermoelectricity.  The experimental data are collected in electromigration break junction where a radical molecule resides.</p