The Kondo Screening Cloud

Renormalization group theory of the Kondo effect predicts that an impurity spin is screened by a conduction electron spread over a large distance of order >.1 to 1 micron. This review has the following sections: 1. The Kondo effect and the screening cloud, 2. Non-observation of the Kondo cloud in conventional experiments, 3. Kondo effect in transmission through a quantum dot, 4. Observing the screening cloud in persistent current experiments, 5. Side-coupled quantum dot, 6. ConclusionsComment: Revtex, 11 pages, 10 postscript figures. To appear in the proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 200

Conformal Field Theory Approach to Quantum Impurity Problems

A brief review is given of a new method for studying the critical behavior of quantum impurity problems, based on conformal field theory techniques, which I developed with Andreas Ludwig. Some results on the overscreened Kondo problem are reviewed. It is shown that the simple open and periodic fixed points, which occur in quantum spin chain impurity models, are related to each other by fusion.Comment: Latex, 15 pages, LaTex, UBCTP-93-25, hard copy of figures available from [email protected]

Edge Magnetic Field in the xxz Spin-1/2 Chain

The critical behavior associated with a transverse magnetic field applied at the edge of a semi-infinite xxz S=1/2 chain is calculated using field theory techniques. Contrary to a recent claim, we find that the long-time behavior is given by a renormalization group fixed point corresponding to an infinite field which polarizes the spin at the edge. The zero temperature entropy and position-dependent magnetization are calculated.Comment: 5 pages, further result added, to appear in J. Phys.

Quantum Impurity Problems in Condensed Matter Physics

Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.Comment: Lecture Notes, Les Houches, 2008, 44 pages. Typos fixed and a new referenc

Boundary Condition Changing Operators in Conformal Field Theory and Condensed Matter Physics

Boundary condition changing operators in conformal field theory describe various types of "sudden switching" problems in condensed matter physics such as the X-ray edge singularity. We review this subject and give two extensions of previous work. A general derivation of a connection between the X-ray edge singularity, the Anderson orthogonality catastrophe and finite-size scaling of energies is given. The formalism is also extended to include boundstates.Comment: 7 pages, RevTex, epsf, for the proceedings of the conference, "Advanced Quantum Field Theory" (in memory of Claude Itzykson) La Londe, France, September, 199

The Kondo screening cloud: what it is and how to observe it

The Kondo effect involves the formation of a spin singlet by a magnetic impurity and conduction electrons. It is characterized by a low temperature scale, the Kondo temperature, $T_K$, and an associated long length scale, $\xi_K = \hbar v_F/(k_BT_K)$ where $v_F$ is the Fermi velocity. This Kondo length is often estimated theoretically to be in the range of .1 to 1 microns but such a long characteristic length scale has never been observed experimentally. In this review, I will examine how $\xi_K$ appears as a crossover scale when one probes either the dependence of physical quantities an distance from the impurity or when the impurity is embedded in a finite size structure and discuss possible experiments that might finally observe this elusive length scale.Comment: Review article for "Perspectives of Mesoscopic Physics - Dedicated to Prof Yoseph Imry's 70th Birthday". Typos correcte

Conformal Field Theory Approach to the Kondo Effect

Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem. In this review some earlier approaches to the Kondo problem are discussed, the needed material on boundary conformal field theory is developed and then this new method is applied to the multi-channel Kondo problem.Comment: 38 pages plus 27 epsf-embedded postscript figures. Lectures given at Summer School in Zakopane, Poland, June, 199

Real fermion modes, impurity entropy, and nontrivial fixed points in the phase diagram of junctions of interacting quantum wires and topological superconductors

We discuss how to extend the impurity entropy to systems with boundary interactions depending on zero-mode real fermion operators (Majorana modes as well as Klein factors). As specific applications of our method, we consider a junction between N interacting quantum wires and a topological superconductor, as well as a Y-junction of three spinless interacting quantum wires. In addition we find a remarkable correspondence between the N=2 topological superconductor junction and the Y-junction. On one hand, this allows us to determine the range of the system parameters in which a stable phase of the N=2 junction is realized as a nontrivial, finite-coupling fixed point corresponding to the M-fixed point in the phase diagram of the Y-junction. On the other hand, it enables us to show the occurrence of a novel "planar" finite-coupling fixed point in the phase diagram of the Y-junction. Eventually, we discuss how to set the system's parameters to realize the correspondence.Comment: 54 pages, 3 .eps figures. Accepted versio

Magnon Wave-function and Impurity Effects in S=1 Antiferromagnetic Chains: A Large-n Approach

A large-n approximation to the S=1 antiferromagnetic chain, using the symmetric tensor representation and its conjugate, is developed to order 1/n in order to calculate the magnon wave-function and to study the effect of modifying the exchange coupling from J to J' on a single link. It is shown that a magnon boundstate exists below the Haldane gap for arbitrarily small negative J'-J but only above a certain critical value of J'-J for positive values. In the former case the binding energy vanishes as the square of (J-J').Comment: revtex, 22 pages, 15 eps figure

Detecting the Kondo screening cloud in conductance measurements on quantum dots

The observation of the Kondo effect in quantum dots has provided new opportunities to finally observe the controversial Kondo screening cloud. We study how screening cloud effects appear in the conductance through a quantum wire containing a quantum dot when the length of the wire is comparable to the size of the screening cloud.Comment: 4 pages in revtex4 format including 4 eps-embedded figure