19 research outputs found
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
CuFe 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 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