468 research outputs found

### Differential equations and duality in massless integrable field theories at zero temperature

Functional relations play a key role in the study of integrable models. We
argue in this paper that for massless field theories at zero temperature, these
relations can in fact be interpreted as monodromy relations. Combined with a
recently discovered duality, this gives a way to bypass the Bethe ansatz, and
compute directly physical quantities as solutions of a linear differential
equation, or as integrals over a hyperelliptic curve. We illustrate these ideas
in details in the case of the $c=1$ theory, and the associated boundary
sine-Gordon model.Comment: 18 pages, harvma

### Critical points in coupled Potts models and critical phases in coupled loop models

We show how to couple two critical Q-state Potts models to yield a new
self-dual critical point. We also present strong evidence of a dense critical
phase near this critical point when the Potts models are defined in their
completely packed loop representations. In the continuum limit, the new
critical point is described by an SU(2) coset conformal field theory, while in
this limit of the the critical phase, the two loop models decouple. Using a
combination of exact results and numerics, we also obtain the phase diagram in
the presence of vacancies. We generalize these results to coupling two Potts
models at different Q.Comment: 23 pages, 10 figure

### Time correlations in 1D quantum impurity problems

We develop in this letter an analytical approach using form- factors to
compute time dependent correlations in integrable quantum impurity problems. As
an example, we obtain for the first time the frequency dependent conductivity
$G(\omega)$ for the tunneling between the edges in the $\nu=1/3$ fractional
quantum Hall effect, and the spectrum $S(w)$ of the spin-spin correlation in
the anisotropic Kondo model and equivalently in the double well system of
dissipative quantum mechanics, both at vanishing temperature.Comment: 4 pages, Revtex and 2 figure

### 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
$SU(2)_q$. 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

### Critical exponents of domain walls in the two-dimensional Potts model

We address the geometrical critical behavior of the two-dimensional Q-state
Potts model in terms of the spin clusters (i.e., connected domains where the
spin takes a constant value). These clusters are different from the usual
Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross
and branch. We develop a transfer matrix technique enabling the formulation and
numerical study of spin clusters even when Q is not an integer. We further
identify geometrically the crossing events which give rise to conformal
correlation functions. This leads to an infinite series of fundamental critical
exponents h_{l_1-l_2,2 l_1}, valid for 0 </- Q </- 4, that describe the
insertion of l_1 thin and l_2 thick domain walls.Comment: 5 pages, 3 figures, 1 tabl

### 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

### Cooper pairs and exclusion statistics from coupled free-fermion chains

We show how to couple two free-fermion chains so that the excitations consist
of Cooper pairs with zero energy, and free particles obeying (mutual) exclusion
statistics. This behavior is reminiscent of anyonic superconductivity, and of a
ferromagnetic version of the Haldane-Shastry spin chain, although here the
interactions are local. We solve this model using the nested Bethe ansatz, and
find all the eigenstates; the Cooper pairs correspond to exact-string or
``0/0'' solutions of the Bethe equations. We show how the model possesses an
infinite-dimensional symmetry algebra, which is a supersymmetric version of the
Yangian symmetry algebra for the Haldane-Shastry model.Comment: 16 pages. v2: includes explicit expression for super-Yangian
generato

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