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

A glimpse of a Luttinger liquid

The concept of a Luttinger liquid has recently been established as a fundamental paradigm vital to our understanding of the properties of one-dimensional quantum systems, leading to a number of theoretical breakthroughs. Now theoretical predictions have been put to test by the comprehensive experimental study.Comment: Unedited version of N&V article in Nature materials 4, 273 (2005

Three-body interactions with cold polar molecules

We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective interaction potentials is based on a microscopic understanding of the underlying molecular physics, and follows from a well controlled and systematic expansion into many-body interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearest-neighbor two-body and three-body interaction. As an illustration, we study the one-dimensional Bose-Hubbard model with dominant three-body interaction and derive its phase diagram.Comment: 8 pages, 4 figure

Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

One of the most remarkable results of quantum mechanics is the fact that many-body quantum systems may exhibit phase transitions even at zero temperature. Quantum fluctuations, deeply rooted in Heisenberg's uncertainty principle, and not thermal fluctuations, drive the system from one phase to another. Typically, the relative strength of two competing terms in the system's Hamiltonian is changed across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry a novel type of quantum phase transition may be induced for which an arbitrarily weak perturbation to the Hamiltonian is sufficient to drive the transition. Here, for a one-dimensional (1D) quantum gas of bosonic caesium atoms with tunable interactions, we observe the commensurate-incommensurate quantum phase transition from a superfluid Luttinger liquid to a Mott-insulator. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model. We trace the phase boundary all the way to the weakly interacting regime where we find good agreement with the predictions of the 1D Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality, and transport phenomena beyond Hubbard-type models in the context of ultracold gases

Noisy Kondo impurities

The anti-ferromagnetic coupling of a magnetic impurity carrying a spin with the conduction electrons spins of a host metal is the basic mechanism responsible for the increase of the resistance of an alloy such as Cu${}_{0.998}$Fe${}_{0.002}$ at low temperature, as originally suggested by Kondo . This coupling has emerged as a very generic property of localized electronic states coupled to a continuum . The possibility to design artificial controllable magnetic impurities in nanoscopic conductors has opened a path to study this many body phenomenon in unusual situations as compared to the initial one and, in particular, in out of equilibrium situations. So far, measurements have focused on the average current. Here, we report on \textit{current fluctuations} (noise) measurements in artificial Kondo impurities made in carbon nanotube devices. We find a striking enhancement of the current noise within the Kondo resonance, in contradiction with simple non-interacting theories. Our findings provide a test bench for one of the most important many-body theories of condensed matter in out of equilibrium situations and shed light on the noise properties of highly conductive molecular devices.Comment: minor differences with published versio

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

Phase Structure and Compactness

In order to study the influence of compactness on low-energy properties, we compare the phase structures of the compact and non-compact two-dimensional multi-frequency sine-Gordon models. It is shown that the high-energy scaling of the compact and non-compact models coincides, but their low-energy behaviors differ. The critical frequency $\beta^2 = 8\pi$ at which the sine-Gordon model undergoes a topological phase transition is found to be unaffected by the compactness of the field since it is determined by high-energy scaling laws. However, the compact two-frequency sine-Gordon model has first and second order phase transitions determined by the low-energy scaling: we show that these are absent in the non-compact model.Comment: 21 pages, 5 figures, minor changes, final version, accepted for publication in JHE

TOULOUSE LIMIT FOR THE OVERSCREENED 4-CHANNEL KONDO PROBLEM

We show that the spin dynamics of the 4--channel Kondo model is equivalent to the one of a model with a spin 1/2 impurity coupled to spin 1 conduction electrons. By abelian bosonization of the latter model we find a kind of Toulouse limit analogous to that recently discussed by Emery and Kivelson for the 2--channel case. We analyse the model by exploiting the close analogy to the problem of an impurity in the Luttinger liquid.Comment: REVTe