Integrability, Non-integrability and confinement

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two approaches, the Form Factor Perturbation Theory and semiclassical methods. Each of them has its own advantage. Using the first approach, one can relate the confinement phenomena of topological excitations to the semi-locality of the operator which breaks integrability. Using the second approach, one can control the bound states which arise in each phase of the theory and predict that their number cannot be more than two.Comment: Invited talk at StatPhys24, Cairns (Australia) 2010. 27 pages, 16 figure

Universal Ratios and Correlation Functions

We review some recent results concerning the quantitative analysis of the universality classes of two-dimensional statistical models near their critical point. We also discuss the exact calculation of the two--point correlation functions of disorder operators in a free theory of complex bosonic and fermionic field, correlators ruled by a Painleve differential equation.Comment: 10 pages, JHEP Proceedings of the Workshop on Integrable Theories, Solitons and Duality, IFT-Unesp, Sao Paulo, Brasi

Stress-Energy Tensor and Ultraviolet Behaviour in Massive Integrable Quantum Field Theories

The short distance behaviour of massive integrable quantum field theories is analyzed in terms of the form factor approach. We show that the on-shell dynamics is compatible with different definitions of the stress-energy tensor $T_{\mu\nu}(x)$ of the theory. In terms of form factors, this is equivalent to having a possible non-zero matrix element $F_1$ of the trace of $T_{\mu\nu}$ on one-particle state. Each choice of $F_1$ induces a different scaling behaviour of the massive theory in the ultraviolet limit.Comment: 32 pages LATEX file (Three figures not included in the text) ISAS/EP/93/6

1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model

The repulsive Lieb-Liniger model can be obtained as the non-relativistic limit of the Sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian and operators) can be put in correspondence with those of the former. We use this mapping, together with the Thermodynamical Bethe Ansatz equations and the exact form factors of the Sinh-Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb-Liniger model both at zero and finite temperature. The computation of one-point correlators is thoroughly detailed and, when possible, compared with known results in the literature.Comment: published version, 27 pages, 10 figure

Mapping between the Sinh-Gordon and Ising Models

The $S$-matrix of the Ising Model can be obtained as particular limit of the roaming trajectories associated to of the $S$-matrix of the Sinh-Gordon model. Using the form factors of the Sinh-Gordon, we analyse the correspondence between the operators of the two theories.Comment: 10 pages, LATEX file, (two figures not included in the text, to be requested separately) IC/93/143, ISAS/EP/93/8

Kink scaling functions in 2D non--integrable quantum field theories

We determine the semiclassical energy levels for the \phi^4 field theory in the broken symmetry phase on a 2D cylindrical geometry with antiperiodic boundary conditions by quantizing the appropriate finite--volume kink solutions. The analytic form of the kink scaling functions for arbitrary size of the system allows us to describe the flow between the twisted sector of c=1 CFT in the UV region and the massive particles in the IR limit. Kink-creating operators are shown to correspond in the UV limit to disorder fields of the c=1 CFT. The problem of the finite--volume spectrum for generic 2D Landau--Ginzburg models is also discussed.Comment: 30 pages, 10 figure

Local Correlations in the Super Tonks-Girardeau Gas

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite temperature we obtain that the three-body correlator has a weak dependence on the temperature up to the degeneracy temperature. We also find that for temperatures larger than the degeneracy temperature the values of the three-body correlator for the super Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar even for relatively small couplings