380 research outputs found
Reflection Matrices for Integrable Supersymmetric Theories
We study two-dimensional integrable supersymmetric theories (without
topological charges) in the presence of a boundary. We find a universal ratio
between the reflection amplitudes for particles that are related by
supersymmetry and we propose exact reflection matrices for the supersymmetric
extensions of the multi-component Yang-Lee models and for the breather
multiplets of the supersymmetric sine-Gordon theory. We point out the
connection between our reflection matrices and the classical boundary actions
for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and
Zhang \cite{IOZ}.Comment: 29 pages, Revtex, 4 figure
Thermodynamic Bethe Ansatz for N = 1 Supersymmetric Theories
We study a series of supersymmetric integrable particle theories in
dimensions. These theories are represented as integrable perturbations
of specific superconformal field theories. Starting from the
conjectured -matrices for these theories, we develop the Thermodynamic Bethe
Ansatz (TBA), where we use that the 2-particle -matrices satisfy a free
fermion condition. Our analysis proves a conjecture by E.~Melzer, who proposed
that these supersymmetric TBA systems are ``folded'' versions of
supersymmetric TBA systems that were first studied by P.~Fendley and
K.~Intriligator.Comment: 24 pages, Revte
A unified framework for the Kondo problem and for an impurity in a Luttinger liquid
We develop a unified theoretical framework for the anisotropic Kondo model
and the boundary sine-Gordon model. They are both boundary integrable quantum
field theories with a quantum-group spin at the boundary which takes values,
respectively, in standard or cyclic representations of the quantum group
. This unification is powerful, and allows us to find new results for
both models. For the anisotropic Kondo problem, we find exact expressions (in
the presence of a magnetic field) for all the coefficients in the
``Anderson-Yuval'' perturbative expansion. Our expressions hold initially in
the very anisotropic regime, but we show how to continue them beyond the
Toulouse point all the way to the isotropic point using an analog of
dimensional regularization. For the boundary sine-Gordon model, which describes
an impurity in a Luttinger liquid, we find the non-equilibrium conductance for
all values of the Luttinger coupling.Comment: 36 pages (22 in double-page format), 7 figures in uuencoded file,
uses harvmac and epsf macro
Supersymmetric Model of Spin-1/2 Fermions on a Chain
In recent work, N=2 supersymmetry has been proposed as a tool for the
analysis of itinerant, correlated fermions on a lattice. In this paper we
extend these considerations to the case of lattice fermions with spin 1/2 . We
introduce a model for correlated spin-1/2 fermions with a manifest N=4
supersymmetry, and analyze its properties. The supersymmetric ground states
that we find represent holes in an anti-ferromagnetic background.Comment: 15 pages, 10 eps figure
Superfrustration of charge degrees of freedom
We review recent results, obtained with P. Fendley, on frustration of quantum
charges in lattice models for itinerant fermions with strong repulsive
interactions. A judicious tuning of kinetic and interaction terms leads to
models possessing supersymmetry. In such models frustration takes the form of
what we call superfrustration: an extensive degeneracy of supersymmetric ground
states. We present a gallery of examples of superfrustration on a variety of 2D
lattices.Comment: 8 pages, 5 figures, contribution to the proceedings of the XXIII
IUPAP International Conference on Statistical Physics (2007) in Genova, Ital
Hyperelliptic curves for multi-channel quantum wires and the multi-channel Kondo problem
We study the current in a multi-channel quantum wire and the magnetization in
the multi-channel Kondo problem. We show that at zero temperature they can be
written simply in terms of contour integrals over a (two-dimensional)
hyperelliptic curve. This allows one to easily demonstrate the existence of
weak-coupling to strong-coupling dualities. In the Kondo problem, the curve is
the same for under- and over-screened cases; the only change is in the contour.Comment: 7 pages, 1 figure, revte
Colored noise in the fractional Hall effect: duality relations and exact results
We study noise in the problem of tunneling between fractional quantum Hall
edge states within a four probe geometry. We explore the implications of the
strong-weak coupling duality symmetry existent in this problem for relating the
various density-density auto-correlations and cross-correlations between the
four terminals. We identify correlations that transform as either ``odd'' or
``anti-symmetric'', or ``even'' or ``symmetric'' quantities under duality. We
show that the low frequency noise is colored, and that the deviations from
white noise are exactly related to the differential conductance. We show
explicitly that the relationship between the slope of the low frequency noise
spectrum and the differential conductance follows from an identity that holds
to {\it all} orders in perturbation theory, supporting the results implied by
the duality symmetry. This generalizes the results of quantum supression of the
finite frequency noise spectrum to Luttinger liquids and fractional statistics
quasiparticles.Comment: 14 pages, 3 figure
Non-equilibrium DC noise in a Luttinger liquid with impurity
We compute exactly the non-equilibrium DC noise in a Luttinger liquid with an
impurity and an applied voltage. By generalizing Landauer transport theory for
Fermi liquids to interacting, integrable systems, we relate this noise to the
density fluctuations of quasiparticles. We then show how to compute these
fluctuations using the Bethe ansatz. The non-trivial density correlations from
the interactions result in a substantial part of the non-equilibrium noise. The
final result for the noise is a scaling function of the voltage, temperature
and impurity coupling. It may eventually be observable in tunneling between
edges of a fractional quantum Hall effect device.Comment: 10 pages with one figure, uses revtex and eps
Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D
We present a full identification of lattice model properties with their field
theoretical counter parts in the continuum limit for a supersymmetric model for
itinerant spinless fermions on a one dimensional chain. The continuum limit of
this model is described by an superconformal field theory
(SCFT) with central charge c=1. We identify states and operators in the lattice
model with fields in the SCFT and we relate boundary conditions on the lattice
to sectors in the field theory. We use the dictionary we develop in this paper,
to give a pedagogical explanation of a powerful tool to study supersymmetric
models based on spectral flow. Finally, we employ the developed machinery to
explain numerically observed properties of the particle density on the open
chain presented in Beccaria et al. PRL 94:100401 (2005).Comment: 28 pages, 7 figures, 3 tables, 1 appendix, this work is based on
chapter 4 of the authors PhD Thesis: L. Huijse, A supersymmetric model for
lattice fermions, University of Amsterdam (2010
Exact non-equilibrium DC shot noise in Luttinger liquids and fractional quantum Hall devices
A point contact in a Luttinger liquid couples the left- and right-moving
channels, producing shot noise. We calculate exactly the DC shot noise at zero
temperature in the out-of-equilibrium steady state where current is flowing.
Integrability of the interaction ensures the existence of a quasiparticle basis
where quasiparticles scatter ``one by one'' off the point contact. This enables
us to apply a direct generalization of the Landauer approach to shot noise to
this interacting model. We find a simple relation of the noise to the current
and the differential conductance. Our results should be experimentally-testable
in a fractional quantum Hall effect device, providing a clear signal of the
fractional charge of the Laughlin quasiparticles.Comment: 4 pages in revtex two-column, one figure
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