Integrable models with unstable particles

We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to integrable models, we subsequently propose a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We describe the general Lie algebraic structure which underlies theories with unstable particles and formulate a decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. We extend these ideas to theories with an infinite spectrum of unstable particles. We provide new expressions for the scattering amplitudes in the soliton-antisoliton sector of the elliptic sine-Gordon model in terms of infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. For that situation we compute the complete S-matrix of all sectors. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal SO(n)-affine Toda field theory

Finite temperature correlation functions from form factors

We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual form factor expansion with the modification of introducing dressing functions of various kinds is only suitable for free theories. Dynamically interacting theories require a more severe change of the form factor program

Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising Model

In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model in the ordered regime, both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions

Decoupling the SU(N)2-homogeneous sine-Gordon model

We provide a systematic construction for all n-particle form factors of the SU(N)2/U(1)N-1-homogeneous sine-Gordon model in terms of general determinant formulas for a large class of local operators. The ultraviolet limit is carried out and the corresponding Virasoro central charge, together with the conformal dimensions of various operators, are identified. The renormalization-group flow is studied and we find a precise rule, depending on the relative order of magnitude of the resonance parameters, according to which the theory decouples into new cosets along the flow

Unstable particles versus resonances in impurity systems, conductance in quantum wires

We compute the DC conductance for a homogeneous sine-Gordon model and an impurity system of Luttinger liquid type by means of the thermodynamic Bethe ansatz and standard potential scattering theory. We demonstrate that unstable particles and resonances in impurity systems lead to a sharp increase of the conductance as a function of the temperature, which is characterized by the Breit-Wigner formula.Comment: 5 pages Latex, 1 figure replaced, version to appear in J. Phys.

Higher particle form factors of branch point twist fields in integrable quantum field theories

In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive 1+1-dimensional integrable quantum field theories and their correlation functions are related to the bi-partite entanglement entropy. We find analytic expressions for some form factors and check those expressions for consistency, mainly by evaluating the conformal dimension of the corresponding twist field in the underlying conformal field theory. We find that solutions to the form factor equations are not unique so that various techniques need to be used to identify those corresponding to the branch point twist field we are interested in. The models for which we carry out our study are characterized by staircase patterns of various physical quantities as functions of the energy scale. As the latter is varied, the beta-function associated to these theories comes close to vanishing at several points between the deep infrared and deep ultraviolet regimes. In other words, renormalisation group flows approach the vicinity of various critical points before ultimately reaching the ultraviolet fixed point. This feature provides an optimal way of checking the consistency of higher particle form factor solutions, as the changes on the conformal dimension of the twist field at various energy scales can only be accounted for by considering higher particle form factor contributions to the expansion of certain correlation functions.Comment: 25 pages, 4 figures; v2 contains small correction

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 $\omega$ 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