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 ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-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 $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-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 ${\cal M}_{2,2n+3}$; 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 $\Phi_{1,3}$. The relation of these ${\bf T}$-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 $S$-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 $m$-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