Quantum integrability of the Alday-Arutyunov-Frolov model

We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. We then show that the quantum integrability of the AAF model follows from this constraint. In the process, we also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments adde

Partial domain wall partition functions

We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call "partial domain wall boundary conditions". We obtain two expressions for the corresponding "partial domain wall partition function", as an (N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP tau-function, and, recalling that these determinants represent tree-level structure constants in N=4 SYM, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure.Comment: 30 pages, LaTeX. This version, which appeared in JHEP, has an abbreviated abstract and some minor stylistic change

On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references adde

The Form Factors and Quantum Equation of Motion in the sine-Gordon Model

Using the methods of the 'form factor program' exact expressions of all matrix elements are obtained for several operators of the quantum sine-Gordon model alias the massive Thirring model. A general formula is presented which provides form factors in terms of an integral representation. In particular charge-less operators as for example the current of the topological charge, the energy momentum tensor and all higher currents are considered. In the breather sector it is found the quantum sine-Gordon field equation holds with an exact relation between the 'bare' mass and the normalized mass. Also a relation for the trace of the energy momentum is obtained. All results are compared with Feynman graph expansion and full agreement is found.Comment: TCI-LaTeX, 21 pages with 2 figur

Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representations of the scalar products of Bethe states of the model.Comment: Latex file, 28 pages, based on the talk given by W. -L. Yang at Statphys 24, Cairns, Australia, 19-23 July, 201

Tailoring Three-Point Functions and Integrability III. Classical Tunneling

We compute three-point functions between one large classical operator and two large BPS operators at weak coupling. We consider operators made out of the scalars of N=4 SYM, dual to strings moving in the sphere. The three-point function exponentiates and can be thought of as a classical tunneling process in which the classical string-like operator decays into two classical BPS states. From an Integrability/Condensed Matter point of view, we simplified inner products of spin chain Bethe states in a classical limit corresponding to long wavelength excitations above the ferromagnetic vacuum. As a by-product we solved a new long-range Ising model in the thermodynamic limit.Comment: 37 pages, 10 figure

Sine-Gordon Model - Renormalization Group Solutions and Applications

The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is carried out through a decomposition of the sine-Gordon field in slow and fast modes. An effective slow modes's theory is derived and re-scaled to obtain the model's flow equations. The resulting Kosterlitz-Thouless phase diagram is obtained and discussed in detail. The theory's gap is estimated in terms of the sine-Gordon model paramaters. The mapping between the sine-Gordon model and models for interacting electrons in one dimension, such as the g-ology model and Hubbard model, is discussed and the previous renormalization group results, obtained for the sine-Gordon model, are thus borrowed to describe different aspects of Luttinger liquid systems, such as the nature of its excitations and phase transitions. The calculations are carried out in a thorough and pedagogical manner, aiming the reader with no previous experience with the sine-Gordon model or the renormalization group approach.Comment: 44 pages, 7 figure

Dynamical Properties of one dimensional Mott Insulators

At low energies the charge sector of one dimensional Mott insulators can be described in terms of a quantum Sine-Gordon model. Using exact results derived from integrability it is possible to determine dynamical properties like the frequency dependent optical conductivity. We compare the exact results to perturbation theory and renormalisation group calculations. We also discuss the application of our results to experiments on quasi-1D organic conductors.Comment: 17 pages, 5 figures, to appear in the proceedings of the NATO ASI/EC summer school "New Theoretical Approaches to Strongly Correlated Systems" Newton Institute for Mathematical Sciences, Cambridge UK, April 200

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.Comment: Review article. v2: published version, 135 pages, 34 figure