25 research outputs found
A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots
The functional renormalization group provides an efficient description of the
interplay and competition of correlations on different energy scales in
interacting Fermi systems. An exact hierarchy of flow equations yields the
gradual evolution from a microscopic model Hamiltonian to the effective action
as a function of a continuously decreasing energy cutoff. Practical
implementations rely on suitable truncations of the hierarchy, which capture
nonuniversal properties at higher energy scales in addition to the universal
low-energy asymptotics. As a specific example we study transport properties
through a single-level quantum dot coupled to Fermi liquid leads. In
particular, we focus on the temperature T=0 gate voltage dependence of the
linear conductance. A comparison with exact results shows that the functional
renormalization group approach captures the broad resonance plateau as well as
the emergence of the Kondo scale. It can be easily extended to more complex
setups of quantum dots.Comment: contribution to Les Houches proceedings 2006, Springer styl
A glimpse of a Luttinger liquid
The concept of a Luttinger liquid has recently been established as a
fundamental paradigm vital to our understanding of the properties of
one-dimensional quantum systems, leading to a number of theoretical
breakthroughs. Now theoretical predictions have been put to test by the
comprehensive experimental study.Comment: Unedited version of N&V article in Nature materials 4, 273 (2005
The one dimensional Kondo lattice model at partial band filling
The Kondo lattice model introduced in 1977 describes a lattice of localized
magnetic moments interacting with a sea of conduction electrons. It is one of
the most important canonical models in the study of a class of rare earth
compounds, called heavy fermion systems, and as such has been studied
intensively by a wide variety of techniques for more than a quarter of a
century. This review focuses on the one dimensional case at partial band
filling, in which the number of conduction electrons is less than the number of
localized moments. The theoretical understanding, based on the bosonized
solution, of the conventional Kondo lattice model is presented in great detail.
This review divides naturally into two parts, the first relating to the
description of the formalism, and the second to its application. After an
all-inclusive description of the bosonization technique, the bosonized form of
the Kondo lattice hamiltonian is constructed in detail. Next the
double-exchange ordering, Kondo singlet formation, the RKKY interaction and
spin polaron formation are described comprehensively. An in-depth analysis of
the phase diagram follows, with special emphasis on the destruction of the
ferromagnetic phase by spin-flip disorder scattering, and of recent numerical
results. The results are shown to hold for both antiferromagnetic and
ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure
Spectral function of a quarter-filled one-dimensional charge density wave insulator.
We consider a one-dimensional charge density wave insulator formed by umklapp processes in a quarter-filled band. The spectrum of the model consists of gapless, uncharged excitations carrying spin +/- 1/2 (spinons) and gapped, spinless excitations carrying charge -/+ signe/2 (solitons and antisolitons). We calculate the low-energy behavior of the single-electron Green's function at zero temperature. The spectral function exhibits a featureless scattering continuum of two solitons and many spinons. The theory predicts that the gap observed by angle resolved photoemission is twice the activation gap in the dc conductivity. We comment on possible applications to PrBa(2)Cu(3)O(7) and to the Bechgaard salts
Dynamical response of quasi 1D Mott insulators
At low energies certain one dimensional Mott insulators can be described in terms of an exactly solvable quantum field theory, the U(1) Thirring model. Using exact results derived from integrability we determine dynamical properties like the frequency dependent optical conductivity and the single-particle Green's function. We discuss the effects of a small temperature and the effects on interchain tunneling in a model of infinitely many weakly coupled chains
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Generalized route to effective field theories for quantum systems with local constraints
Some of the exciting phenomena uncovered in strongly correlated systems in
recent years - for instance quantum topological order, deconfined quantum
criticality, and emergent gauge symmetries -- appear in systems in which the
Hilbert space is effectively projected at low energies in a way that imposes
local constraints on the original degrees of freedom. Cases in point include
spin liquids, valence bond systems, dimer models, and vertex models. In this
work, we use a slave boson description coupled to a large- path integral
formulation to devise a generalised route to obtain effective field theories
for such systems. We demonstrate the validity and capability of our approach by
studying quantum dimer models and by comparing our results with the existing
literature. Field-theoretic approaches to date are limited to bipartite
lattices, they depend on a gauge-symmetric understanding of the constraint, and
they lack generic quantitative predictive power for the coefficients of the
terms that appear in the Lagrangians of these systems. Our method overcomes all
these shortcomings and we show how the results up to quadratic order compare
with the known height description of the square lattice quantum dimer model, as
well as with the numerical estimate of the speed of light of the photon
excitations on the diamond lattice. Finally, instanton considerations allow us
to infer properties of the finite-temperature behaviour in two dimensions
Finite wave vector pairing in doped two-leg ladders
We consider the effects of Umklapp processes in doped two-leg fermionic ladders. These may emerge either at special band fillings or as a result of the presence of external periodic potentials. We show that such Umklapp processes can lead to profound changes of physical properties and in particular stabilize pair-density wave phases