The W1+∞W_{1 + \infty } effective theory of the Calogero- Sutherland model and Luttinger systems.

We construct the effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles $N$. It is given by a \winf conformal field theory (with central charge $c=1$) that describes {\it exactly} the spatial density fluctuations arising from the low-energy excitations about the Fermi surface. Our approach does not rely on the integrable character of the model, and indicates how to extend previous results to any order in powers of $1/N$. Moreover, the same effective theory can also be used to describe an entire universality class of $(1+1)$-dimensional fermionic systems beyond the Calogero-Sutherland model, that we identify with the class of {\it chiral Luttinger systems}. We also explain how a systematic bosonization procedure can be performed using the \winf generators, and propose this algebraic approach to {\it classify} low-dimensional non-relativistic fermionic systems, given that all representations of \winf are known. This approach has the appeal of being mathematically complete and physically intuitive, encoding the picture suggested by Luttinger's theorem.Comment: 13 pages, plain LaTeX, no figures

The extended conformal theory of the Calogero-Sutherland model

We describe the recently introduced method of Algebraic Bosonization of (1+1)-dimensional fermionic systems by discussing the specific case of the Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also presented.Comment: 12 pages, plain LaTeX, no figures; To appear in the proceedings of the IV Meeting "Common Trends in Condensed Matter and High Energy Physics", Chia Laguna, Cagliari, Italy, 3-10 Sep. 199

Symmetry Aspects and Finite-Size Scaling of Quantum Hall Fluids

The exactness and universality observed in the quantum Hall effect suggests the existence of a symmetry principle underlying Laughlin's theory. We review the role played by the infinite $W_{\infty }$ and conformal algebras as dynamical symmetries of incompressible quantum fluids and show how they predict universal finite-size effects in the excitation spectrum.Comment: 15 pages, CERN-TH-6784/93, LateX fil

The extended conformal theory of Luttinger systems

We describe the recently introduced method of algebraic bosonization of the $(1+1)$-dimensional Luttinger systems by discussing in detail the specific case of the Calogero-Sutherland model, and mentioning the hard-core Bose gas. We also compare our findings with the exact Bethe Ansatz results.Comment: 9 pages, plain Latex file, ,based on a talk given by S. Sciuto at the II International Sakharov Conference on Physics, Moscow, Russia, 20-24 May 9

Chiral Partition Functions of Quantum Hall Droplets

Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and non-Abelian Read-Rezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, involving charged and neutral parts, and the fusion rules.Comment: 37 pages, 8 figure

Effective Field Theories for Electrons in Crystalline Structures

We present an effective field theory formulation for a class of condensed matter systems with crystalline structures for which some of the discrete symmetries of the underlying crystal survive the long distance limit, up to mesoscopic scales, and argue that this class includes interesting materials, such as $Si$-doped $GaAs$. The surviving symmetries determine a limited set of possible effective interactions, that we analyze in detail for the case of $Si$-doped $GaAs$ materials. These coincide with the ones proposed in the literature to describe the spin relaxation times for the $Si$-doped $Ga As$ materials, obtained here as a consequence of the choice of effective fields and their symmetries. The resulting low-energy effective theory is described in terms of three (six chiral) one-dimensional Luttinger liquid systems and their corresponding intervalley transitions. We also discuss the Mott transition within the context of the effective theory.Comment: 24 pages, 3 figure

Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure

Neutral modes edge state dynamics through quantum point contacts

Dynamics of neutral modes for fractional quantum Hall states is investigated for a quantum point contact geometry in the weak-backscattering regime. The effective field theory introduced by Fradkin-Lopez for edge states in the Jain sequence is generalized to the case of propagating neutral modes. The dominant tunnelling processes are identified also in the presence of non-universal phenomena induced by interactions. The crossover regime in the backscattering current between tunnelling of single-quasiparticles and of agglomerates of p-quasiparticles is analysed. We demonstrate that higher order cumulants of the backscattering current fluctuations are a unique resource to study quantitatively the competition between different carrier charges. We find that propagating neutral modes are a necessary ingredient in order to explain this crossover phenomena.Comment: 28 pages, 5 figure