Point-like topological defects in bilayer quantum Hall systems

Following a suggestion given in Phys. Lett. B 571 (2003) 250, we show how a bilayer Quantum Hall system at fillings nu =m/pm+2 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (cond-mat/0503478) which evidence the presence of a topological defect in the bilayer system.Comment: 9 pages, 3 figure

A dual 2D model for the Quantum Hall Fluid

We present a dual two dimensional model for the Quantum Hall Fluid depending on two parameters and show that this model has topologically non-trivial vacua which are infrared stable fixed points of the Renormalization Group. The model has a discrete (modular) symmetry which reproduces the fenomenological law of corresponding states and allows for an unified description of the critical points corresponding to Hall plateaus in terms of a 2 dimensional Conformal Field Theory.Comment: 10 pages, Revtex, no figure

Paired states on a torus

We analyze the modular properties of the effective CFT description for paired states, proposed in cond-mat/0003453, corresponding to the non-standard filling nu =1/(p+1). We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering our partition function naturally go to complete a Z_2-orbifold construction of the CFT for the Halperin state. Different behaviours for the p even and p odd cases are also studied. Finally it is shown that the tunneling phenomenon selects out a twist invariant CFT which is identified with the Moore-Read model.Comment: 24 pages, 1 figure, Late

A conformal field theory description of the paired and parafermionic states in the quantum Hall effect

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in cond-mat/9912287 to the description of a quantum Hall fluid at non standard fillings nu=m/(pm+2). The chiral primary fields are found by using a procedure which induces twisted boundary conditions on the m scalar fields; they appear as composite operators of a charged and neutral component. The neutral modes describe parafermions and contribute to the ground state wave function with a generalized Pfaffian term. Correlators of Ne electrons in the presence of quasi-hole excitations are explicitly given for m=2.Comment: 11 pages, plain Late

A conformal field theory description of magnetic flux fractionalization in Josephson junction ladders

We show how the recently proposed effective theory for a Quantum Hall system at "paired states" filling v=1 (Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B641 (2002) 547), the twisted model (TM), well adapts to describe the phenomenology of Josephson Junction ladders (JJL) in the presence of defects. In particular it is shown how naturally the phenomenon of flux fractionalization takes place in such a description and its relation with the discrete symmetries present in the TM. Furthermore we focus on closed geometries, which enable us to analyze the topological properties of the ground state of the system in relation to the presence of half flux quanta.Comment: 16 pages, 2 figure, Latex, revised versio

Topological order in Josephson junction ladders with Mobius boundary conditions

We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions, in particular we show how such a system can develop topological order. Such a property is crucial for its implementation as a "protected" solid state qubit.Comment: 14 pages, 3 figures, to appear in JSTA

New Results on the Phase Diagram of the FFXY Model: A Twisted CFT Approach

The issue of the number, nature and sequence of phase transitions in the fully frustrated XY (FFXY) model is a highly non trivial one due to the complex interplay between its continuous and discrete degrees of freedom. In this contribution we attack such a problem by means of a twisted conformal field theory (CFT) approach and show how it gives rise to the U (1)$\otimes Z_{2}$ symmetry and to the whole spectrum of excitations of the FFXY model.Comment: 7 pages; talk given by G. Niccoli at "Path Integrals - New Trends and Perspectives International Conference", Max-Planck-Institut, Dresden, Germany, September 23 - 28, 200

A twisted conformal field theory description of the Quantum Hall Effect

We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows to describe a quantum Hall fluid at Jain hierarchical filling, nu=m/(2pm+1), in terms of one charged scalar field and m-1 neutral ones. Then the resulting algebra of the chiral primary fields is U(1)xW_m. Finally the ground state wave functions are given as correlators of appropriate composite fields (a-electrons).Comment: 11 pages, plain Late

Dissipative quantum mechanics and Kondo-like impurities on noncommutative two-tori

In a recent paper, by exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter $\theta$ (in appropriate units), a general one-to-one correspondence between the $m$-reduced conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings $\nu =\frac{m}{pm+2}$ and an Abelian noncommutative field theory (NCFT) has been established . That allowed us to add new evidence to the relationship between noncommutativity and quantum Hall fluids\cite% {ncmanybody}. On the other hand, the $m$-reduced CFT is equivalent to a system of two massless scalar bosons with a magnetic boundary interaction as introduced by Callan et al., at the so called ``magic''\ points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Here we develop such a point of view by focusing on the case $m=2$ which corresponds to a quantum Hall bilayer. The key role of a localized impurity which couples the two layers is emphasized and the effect of noncommutativity in terms of generalized magnetic translations (GMT) is fully exploited. As a result, general GMT operators are introduced, in the form of a tensor product, which act on the QHF and defect space respectively, and a comprehensive study of their rich structure is performed.Comment: 18 pages, 1 figure, accepted for publication in International Journal of Modern Physics

MOND's acceleration scale as a fundamental quantity

Some quantum-cosmic scaling relations indicate that the MOND acceleration parameter a_0 could be a fundamental quantity ruling the self-gravitating structures, ranging from stars and globular clusters up to superclusters of galaxies and the whole observed universe. We discuss such coincidence relations starting from the Dirac quantization condition ruling the masses of primordial black holes.Comment: 6 page