231 research outputs found
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
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
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]
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, , and an associated long length scale,
where 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 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
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.
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
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
A fermionic approach to tunneling through junctions of multiple quantum wires
Junctions of multiple one-dimensional quantum wires of interacting electrons
have received considerable theoretical attention as a basic constituent of
quantum circuits. While results have been obtained on these models using
bosonization and Density Matrix Renormalization Group (DMRG) methods, another
powerful technique is based on direct perturbation theory in the bulk
interactions, combined with the Renormalization Group (RG) and summed in the
Random Phase Approximation (RPA). This technique has so far only been applied
to the case where finite length interacting wires are attached to
non-interacting Fermi liquid leads. We reformulate it in terms of the
single-particle S-matrix, formally unifying treatments of junctions of
different numbers of leads, and extend this method to cover the case of
infinite length interacting leads obtaining results on 2-lead and 3-lead
junctions in good agreement with previous bosonization and DMRG results.Comment: 24 pages, 5 figures; v
Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
A lattice of interacting Majorana modes can occur in a superconducting film
on a topological insulator in a magnetic field. The phase diagram as a function
of interaction strength for the square lattice was analyzed recently using a
combination of mean field theory and renormalization group methods, and was
found to include second order phase transitions. One of these corresponds to
spontaneous breaking of an emergent U(1) symmetry, for attractive interactions.
Despite the fact that the U(1) symmetry is not exact, this transition was
claimed to be in a supersymmetric universality class when time reversal
symmetry is present and in the conventional XY universality class otherwise.
Another second order transition was predicted for repulsive interactions with
time reversal symmetry to be in the same universality class as the transition
occurring in the Gross-Neveu model, despite the fact that the U(1) symmetry is
not exact in the Majorana model. We analyze these phase transitions using a
modified -expansion, confirming the previous conclusions.Comment: 13 pages + 13 pages of appendice
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