132 research outputs found
Transport Properties of Multiple Quantum Dots Arranged in Parallel: Results from the Bethe Ansatz
In this paper we analyze transport through a double dot system connected to
two external leads. Imagining each dot possessing a single active level, we
model the system through a generalization of the Anderson model. We argue that
this model is exactly solvable when certain constraints are placed upon the dot
Coulomb charging energy, the dot-lead hybridization, and the value of the
applied gate voltage. Using this exact solvability, we access the zero
temperature linear response conductance both in and out of the presence of a
Zeeman field. We are also able to study the finite temperature linear response
conductance. We focus on universal behaviour and identify three primary
features in the transport of the dots: i) a so-called RKKY Kondo effect; ii) a
standard Kondo effect; and iii) interference phenomena leading to sharp
variations in the conductance including conductance zeros. We are able to use
the exact solvability of the dot model to characterize these phenomena
quantitatively. While here we primarily consider a double dot system, the
approach adopted applies equally well to N-dot systems.Comment: 28 pages, 10 figures; references added in v
Purely transmitting integrable defects
Some aspects of integrable field theories possessing purely transmitting
defects are described. The main example is the sine-Gordon model and several
striking features of a classical field theory containing one or more defects
are pointed out. Similar features appearing in the associated quantum field
theory are also reviewed briefly.Comment: 6 pages, to appear in Proceedings of the XVth International
Colloquium on Integrable Systems and Quantum Symmetries, Prague, June 200
Doped Spin Liquid: Luttinger Sum Rule and Low Temperature Order
We analyze a model of two-leg Hubbard ladders weakly coupled by interladder
tunneling. At half filling a semimetallic state with small Fermi pockets is
induced beyond a threshold tunneling strength. The sign changes in the single
electron Green's function relevant for the Luttinger Sum Rule now take place at
surfaces with both zeroes and infinities with important consequences for the
interpretation of ARPES experiments. Residual interactions between electron and
hole-like quasi-particles cause a transition to long range order at low
temperatures. The theory can be extended to small doping leading to
superconducting order.Comment: 4 pages, 3 figure
The Scattering Theory of Oscillator Defects in an Optical Fiber
We examine harmonic oscillator defects coupled to a photon field in the
environs of an optical fiber. Using techniques borrowed or extended from the
theory of two dimensional quantum fields with boundaries and defects, we are
able to compute exactly a number of interesting quantities. We calculate the
scattering S-matrices (i.e. the reflection and transmission amplitudes) of the
photons off a single defect. We determine using techniques derived from
thermodynamic Bethe ansatz (TBA) the thermodynamic potentials of the
interacting photon-defect system. And we compute several correlators of
physical interest. We find the photon occupancy at finite temperature, the
spontaneous emission spectrum from the decay of an excited state, and the
correlation functions of the defect degrees of freedom. In an extension of the
single defect theory, we find the photonic band structure that arises from a
periodic array of harmonic oscillators. In another extension, we examine a
continuous array of defects and exactly derive its dispersion relation. With
some differences, the spectrum is similar to that found for EM wave propagation
in covalent crystals. We then add to this continuum theory isolated defects, so
as to obtain a more realistic model of defects embedded in a frequency
dependent dielectric medium. We do this both with a single isolated defect and
with an array of isolated defects, and so compute how the S-matrices and the
band structure change in a dynamic medium.Comment: 32 pages, TeX with harvmac macros, three postscript figure
Duality approach to one-dimensional degenerate electronic systems
We investigate the possible classification of zero-temperature spin-gapped
phases of multicomponent electronic systems in one spatial dimension. At the
heart of our analysis is the existence of non-perturbative duality symmetries
which emerge within a low-energy description. These dualities fall into a
finite number of classes that can be listed and depend only on the algebraic
properties of the symmetries of the system: its physical symmetry group and the
maximal continuous symmetry group of the interaction. We further characterize
possible competing orders associated to the dualities and discuss the nature of
the quantum phase transitions between them. Finally, as an illustration, the
duality approach is applied to the description of the phases of two-leg
electronic ladders for incommensurate filling.Comment: 53 pages, 3 figures, published versio
Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions
We study both the static and dynamic properties of gapped, one-dimensional,
Heisenberg, anti-ferromagnetic, spin chains at finite temperature through an
analysis of the O(3) non-linear sigma model. Exploiting the integrability of
this theory, we are able to compute an exact low temperature expansion of the
finite temperature correlators. We do so using a truncated `form-factor'
expansion and so provide evidence that this technique can be successfully
extended to finite temperature. As a direct test, we compute the static
zero-field susceptibility and obtain an exact match to the susceptibility
derived from the low temperature expansion of the exact free energy. We also
study transport properties, computing both the spin conductance and the
NMR-relaxation rate, 1/T_1. We find these quantities to show ballistic
behaviour. In particular, the computed spin conductance exhibits a non-zero
Drude weight at finite temperature and zero applied field. The physics thus
described differs from the spin diffusion reported by Takigawa et al. from
experiments on the Haldane gap material, AgVP_2S_6.Comment: 51 pages, 5 figure
Applications of quantum integrable systems
We present two applications of quantum integrable systems. First, we predict
that it is possible to generate high harmonics from solid state devices by
demostrating that the emission spectrum for a minimally coupled laser field of
frequency to an impurity system of a quantum wire, contains multiples
of the incoming frequency. Second, evaluating expressions for the conductance
in the high temperature regime we show that the caracteristic filling fractions
of the Jain sequence, which occur in the fractional quantum Hall effect, can be
obtained from quantum wires which are described by minimal affine Toda field
theories.Comment: 25 pages of LaTex, 4 figures, based on talk at the 6-th international
workshop on conformal field theories and integrable models, (Chernogolovka,
September 2002
Finite temperature dynamics of the Anderson model
The recently introduced local moment approach (LMA) is extended to encompass
single-particle dynamics and transport properties of the Anderson impurity
model at finite-temperature, T. While applicable to arbitrary interaction
strengths, primary emphasis is given to the strongly correlated Kondo regime
(characterized by the T=0 Kondo scale ). In particular the
resultant universal scaling behaviour of the single-particle spectrum
D(\omega; T) \equiv F(\frac{\w}{\omega_{\rm K}}; \frac{T}{\omega_{\rm K}})
within the LMA is obtained in closed form; leading to an analytical description
of the thermal destruction of the Kondo resonance on all energy scales.
Transport properties follow directly from a knowledge of . The -dependence of the resulting resistivity , which is
found to agree rather well with numerical renormalization group calculations,
is shown to be asymptotically exact at high temperatures; to concur well with
the Hamann approximation for the s-d model down to ,
and to cross over smoothly to the Fermi liquid form in the low-temperature limit. The underlying
approach, while naturally approximate, is moreover applicable to a broad range
of quantum impurity and related models
Haldane-Gapped Spin Chains as Luttinger Liquids: Correlation Functions at Finite Field
We study the behavior of Heisenberg, antiferromagnetic, integer-spin chains
in the presence of a magnetic field exceeding the attendant spin gap. For
temperatures much smaller than the gap, the spin chains exhibit Luttinger
liquid behavior. We compute exactly both the corresponding Luttinger parameter
and the Fermi velocity as a function of magnetic field. This enables the
computation of a number of correlators from which we derive the spin
conductance, the expected form of the dynamic structure factor relevant to
inelastic neutron scattering experiments, and NMR relaxation rates. We also
comment upon the robustness of the magnetically induced gapless phase both to
finite temperature and finite couplings between neighbouring chains.Comment: 32 pages, 8 figures; published version includes additions discussing
the robustness of the magnetically induced gapless phase to ordering between
chains as well as the relationship between the spin-1 chains and spin-1/2
ladders in the presence of a magnetic fiel
The sine-Gordon model with integrable defects revisited
Application of our algebraic approach to Liouville integrable defects is
proposed for the sine-Gordon model. Integrability of the model is ensured by
the underlying classical r-matrix algebra. The first local integrals of motion
are identified together with the corresponding Lax pairs. Continuity conditions
imposed on the time components of the entailed Lax pairs give rise to the
sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment
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