Gerardo Cristofano

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 one to describe a quantum Hall fluid at Jain hierarchical filling, , in terms of one charged scalar field and m - 1 neutral ones. Then the resulting algebra of the chiral primary fields is U(1)×. Finally the ground state wave functions are given as correlators of appropriate composite fields (a-electrons).

Twisted CFT and bilayer quantum Hall systems in the presence of an impurity

Abstract We identify the impurity interactions of the recently proposed CFT description of a bilayer quantum Hall system at filling ν= m pm+2 [Mod. Phys. Lett. A 15 (2000) 1679]. Such a CFT is obtained by m -reduction on the one layer system, with a resulting pairing symmetry and presence of quasi-holes. For the m =2 case boundary terms are shown to describe an impurity interaction which allows for a localized tunnel of the Kondo problem type. The presence of an anomalous fixed point is evidenced at finite coupling which is unstable with respect to unbalance and flows to a vacuum state with no quasi-holes.

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 Ref. 1 to the description of a quantum Hall fluid at nonstandard fillings . 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.

Astrophysical structures from primordial quantum black holes

The characteristic sizes of astrophysical structures, up to the whole observed Universe, can be recovered, in principle, assuming that gravity is the overall interaction assembling systems starting from microscopic scales, whose order of magnitude is ruled by the Planck length and the related Compton wavelength. This result agrees with the absence of screening mechanisms for the gravitational interaction and could be connected to the presence of Yukawa corrections in the Newtonian potential which introduce typical interaction lengths. This result directly comes out from quantization of primordial black holes and then characteristic interaction lengths directly emerge from quantum field theory.

A twisted conformal field theory description of dissipative quantum mechanics

Abstract We show how the recently proposed CFT for a bilayer quantum Hall system at filling ν= m pm+2 [Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B 641 (2002) 547; Phys. Lett. B 571 (2003) 250], the twisted model (TM), is equivalent to the system of two massless scalar bosons with a magnetic boundary interaction as introduced in [Nucl. Phys. B 443 (1995) 444], 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. Such an analogy is further developed in terms of the TM boundary states, by describing the interaction between an impurity with a Hall system.

TUNNELING EFFECTS IN A BRANE SYSTEM AND QUANTUM HALL PHYSICS

We argue that a system of interacting D-branes, generalizing a recent proposal, can be modeled as a quantum Hall fluid. We show that tachyon condensation in such a system is equivalent to one-particle tunneling. In a conformal field theory effective description, that induces a transition from a theory with central charge c = 2 to a theory with c = 3/2, with a corresponding symmetry enhancement.

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.

Point-like topological defects in bilayer quantum Hall systems

Following a suggestion given in Cristofano et al (2003 Phys. Lett. B 571 250; 2004 Nucl. Phys. B 679 621), we show how a bilayer quantum Hall system at fillings ν = 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 of Deviatov et al (2005 Phys. Rev. B 72 041305) which evidence the presence of a topological defect in the bilayer system.

Jain states on a torus: an unifying description

We analyze the modular properties of the effective CFT description for Jain plateaux, proposed in [1], corresponding to the fillings ν = m/(2pm+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 the partition function go to complete a Z m -orbifold construction of the RCFT (1) × u(m)1 proposed for the Jain states [2,3]. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT extension of the (1) × m minimal models [3]. For m = 2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models (1) × 2 .

Fully frustrated Josephson junction ladders with Mobius boundary conditions as topologically protected qubits

Abstract We show how to realize a “protected” qubit by using a fully frustrated Josephson junction ladder (JJL) with Mobius boundary conditions. Such a system has been recently studied within a twisted conformal field theory (CFT) approach [G. Cristofano, G. Maiella, V. Marotta, Mod. Phys. Lett. A 15 (2000) 1679; G. Cristofano, G. Maiella, V. Marotta, G. Niccoli, Nucl. Phys. B 641 (2002) 547] and shown to develop the phenomenon of flux fractionalization [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Eur. Phys. J. B 49 (2006) 83]. The relevance of a “closed” geometry has been fully exploited in relating the topological properties of the ground state of the system to the presence of half flux quanta and the emergence of a topological order has been predicted [G. Cristofano, V. Marotta, A. Naddeo, J. Stat. Mech.: Theory Exp. (2005) P03006]. In this Letter the stability and transformation properties of the ground states under adiabatic magnetic flux change are analyzed and the deep consequences on the realization of a solid state qubit, protected from decoherence, are presented.