36 research outputs found
Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz
We prove that the solution to a pair of nonlinear integral equations arising
in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent
kernel of the linear integral operator with kernel
exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]Comment: 16 pages, LaTeX file, no figures. Revision has minor change
Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
We construct the quantum versions of the monodromy matrices of KdV theory.
The traces of these quantum monodromy matrices, which will be called as ``-operators'', act in highest weight Virasoro modules. The -operators depend on the spectral parameter and their expansion
around generates an infinite set of commuting Hamiltonians
of the quantum KdV system. The -operators can be viewed as the
continuous field theory versions of the commuting transfer-matrices of
integrable lattice theory. In particular, we show that for the values
of the Virasoro central charge
the eigenvalues of the -operators satisfy a closed system of
functional equations sufficient for determining the spectrum. For the
ground-state eigenvalue these functional equations are equivalent to those of
massless Thermodynamic Bethe Ansatz for the minimal conformal field theory
; in general they provide a way to generalize the technique
of Thermodynamic Bethe Ansatz to the excited states. We discuss a
generalization of our approach to the cases of massive field theories obtained
by perturbing these Conformal Field Theories with the operator .
The relation of these -operators to the boundary states is also
briefly described.Comment: 24 page
RG Flows from Super-Liouville Theory to Critical Ising Model
We study an integrable deformation of the super-Liouville theory which
generates a RG flows to the critical Ising model as the IR fixed point. This
model turns out to be a supersymmetric sinh-Gordon model with spontaneously
broken N=1 supersymmetry. The resulting massless Goldstino is the only stable
on-shell particle which controls the IR behaviours. We propose the exact
-matrix of the Goldstino and compare associated thermodynamic Bethe ansatz
equations with the quantization conditions derived from the reflection
amplitudes of the the super-Liouville theory to provide nonperturbative checks
for both the (NS) and the (R) sectors.Comment: 10 pages, 1 figures, to be published in Phys. Lett.
Y-System and Deformed Thermodynamic Bethe Ansatz
We introduce a new tool, the Deformed TBA (Deformed Thermodynamic Bethe
Ansatz), to analyze the monodromy problem of the cubic oscillator. The Deformed
TBA is a system of five coupled nonlinear integral equations, which in a
particular case reduces to the Zamolodchikov TBA equation for the 3-state Potts
model. Our method generalizes the Dorey-Tateo analysis of the (monomial) cubic
oscillator. We introduce a Y-system corresponding to the Deformed TBA and give
it an elegant geometric interpretation.Comment: 12 pages. Minor corrections in Section
Tunneling gap of laterally separated quantum Hall states
We use a method of matched asymptotics to determine the energy gap of two
counter-propagating, strongly interacting, quantum Hall edge states. The
microscopic edge state dispersion and Coulomb interactions are used to
precisely constrain the short-distance behavior of an integrable field theory,
which then determines the low energy spectrum. We discuss the relationship of
our results to the tunneling measurements of Kang et al., Nature 403, 59
(2000).Comment: 4 pages, 1 figur
Constructing Infinite Particle Spectra
We propose a general construction principle which allows to include an
infinite number of resonance states into a scattering matrix of hyperbolic
type. As a concrete realization of this mechanism we provide new S-matrices
generalizing a class of hyperbolic ones, which are related to a pair of simple
Lie algebras, to the elliptic case. For specific choices of the algebras we
propose elliptic generalizations of affine Toda field theories and the
homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model
we compute explicitly renormalization group scaling functions by means of the
c-theorem and the thermodynamic Bethe ansatz. In particular we identify the
Virasoro central charges of the corresponding ultraviolet conformal field
theories.Comment: 7 pages Latex, 7 figures (typo in figure 3 corrected
Bosonization Theory of Excitons in One-dimensional Narrow Gap Semiconductors
Excitons in one-dimensional narrow gap semiconductors of anti-crossing
quantum Hall edge states are investigated using a bosonization method. The
excitonic states are studied by mapping the problem into a non-integrable
sine-Gordon type model. We also find that many-body interactions lead to a
strong enhancement of the band gap. We have estimated when an exciton
instability may occur.Comment: 4pages, 1 figure, to appear in Phys. Rev. B Brief Report
Coulomb Blockade Regime of a Single-Wall Nanotube
A model of carbon nanotube at half filling is studied. The Coulomb
interaction is assumed to be unscreened. It is shown that this allows to
develop the adiabatic approximation which leads to considerable simplifications
in calculations of the excitation spectrum. We give a detailed analysis of the
spectrum and the phase diagram at half filling and discuss effects of small
doping. At small doping several phases develop strong superconducting
fluctuations corresponding to various types of pairing
Dynamical Structure Factor in Cu Benzoate and other spin-1/2 antiferromagnetic chains
Recent experiments of the quasi-one-dimensional spin-1/2 antiferromagnet
Copper Benzoate established the existence of a magnetic field induced gap. The
observed neutron scattering intensity exhibits resolution limited peaks at both
the antiferromagnetic wave number and at incommensurate wave numbers related to
the applied magnetic field. We determine the ratio of spectral weights of these
peaks within the framework of a low-energy effective field theory description
of the problem.Comment: 5 pages, 3figure
New Criticality of 1D Fermions
One-dimensional massive quantum particles (or 1+1-dimensional random walks)
with short-ranged multi-particle interactions are studied by exact
renormalization group methods. With repulsive pair forces, such particles are
known to scale as free fermions. With finite -body forces (m = 3,4,...), a
critical instability is found, indicating the transition to a fermionic bound
state. These unbinding transitions represent new universality classes of
interacting fermions relevant to polymer and membrane systems. Implications for
massless fermions, e.g. in the Hubbard model, are also noted. (to appear in
Phys. Rev. Lett.)Comment: 10 pages (latex), with 2 figures (not included