Marotta Vincenzo

• Prof
• Research Associate at INFN - Istituto Nazionale di Fisica Nucleare

We review our recent results on the physics of quantum Hall fluids at Jain and non conventional fillings within a general field theoretic framework. We focus on a peculiar conformal field theory (CFT), the one obtained by means of the m-reduction technique, and stress its power in describing strongly correlated low dimensional condensed matter syst...

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 θ (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 fillings1,2...

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting...

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 one-to-one correspondence between an abelian noncommutative field theory (NCFT) and a non-abelian theory of twisted fields on ordinary space can be established. Start...

The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter θ (in appropriate units): an isomorphism is established between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space. We focus on a particular conforma...

The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter theta (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a non-abelian theory of twisted fields on ordinary space. We focus on a particular conf...

We show how the low energy properties of the two-leg XXZ spin-1/2 ladders with general anisotropy parameter Δ on closed geometries can be accounted for in the framework of the m-reduction procedure developed previously (Cristofano et al 2000 Mod. Phys. Lett. A 15 547; Cristofano et al 2000 Mod. Phys. Lett. A 15 1679; Cristofano et al 2002 Nucl. Phy...

We show how the low-energy properties of the 2-leg XXZ spin-1/2 ladders with general anisotropy parameter $\Delta $ on closed geometries can be accounted for in the framework of the m-reduction procedure developed in [1]. In the limit of quasi-decoupled chains, a conformal field theory (CFT) with central charge c=2 is derived and its ability to des...

shown to develop the phenomenon of flux fractionalization [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Eur. Phys. J. B 49 (2006) 83]. That led us to predict the emergence of a topological order in such a system [G. Cristofano, V. Marotta, A. Naddeo, J. Stat. Mech.: Theory Exp. (2005) P03006]. In this Letter we analyze the ground states and th...

We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $\theta $ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and a nonabelian theory of twisted fields on ordinary space. We concentrate on a particular conformal field theor...

Recently a one-dimensional closed ladder of Josephson junctions has been studied (G. Cristofano et al., Phys. Lett. A 372 (2008) 2464) within a twisted conformal field theory (CFT) approach (G. Cristofano et al., Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B 641 (2002) 547) and shown to develop the phenomenon of flux fractionalization (G. Cristo...

We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter θ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and a nonabelian theory of twisted fields on ordinary space. We concentrate on a particular conformal field theory (CFT),...

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. shown to develop the phenomenon of flux fractionalization [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Eur. P...

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 ris...

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 (Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B 641 (2002) 547) and shown to develop the phenomenon of flux fractio...

Following an earlier suggestion, we show how the U (1) ⊗ Z 2 symmetry of the fully frustrated XY (F F XY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at 'paired states' fillings ν = 1. The resulting twisted conformal field theory (CFT) with central charge c = 2 is...

Following a suggestion given in [1], we show how a bilayer Quantum Hall system at fillings v = 1 p+1 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 re...

Following a suggestion given in Nucl. Phys. B 300 (1988)611,we show how the U(1)*Z_{2} symmetry of the fully frustrated XY (FFXY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at "paired states" fillings nu =1 (cfr. Cristofano et al.,Mod. Phys. Lett. A 15 (2000)1679;...

We found new identities among the Dedekind η-function, the characters of the m algebra and those of the level 1 affine Lie algebra . They allow to characterize the m-orbifold of the m-component free bosons (our theory TM) as an extension of the fully degenerate representations of W1+∞(m). In particular, TM is proven to be a Γθ-RCFT extension of th...

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...

We show how the recently proposed effective theory for a Quantum Hall system at “paired states” filling ν=1 [1,2], 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 de...

How a one-dimensional fully frustrated ladder of quantum Josephson junctions may develop quantum order is shown here. Such a property is crucial for its implementation as a protected solid state qubit.

We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions (see cond-mat/0503555; we show how such a system can develop topological order thanks to flux fractionalization. Such a property is crucial for its implementation as a "protected" solid state qubit.

We review the main results of the effective description of the Quantum Hall fluid for the Jain fillings, nu=m/2pm+1, and the non-standard ones nu=m/pm+2 by a conformal field theory (CFT) in two dimensions. It is stressed the unifying character of the m-reduction procedure to construct appropriate twisted CFT models, called Twisted Models (TM), whic...

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...

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.

We analyze the modular properties of the effective CFT description for Jain plateaux corresponding to the fillings nu=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...

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 (199...

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 descri...

We identify the impurity interactions of the recently proposed CFT description of a bilayer Quantum Hall system at filling ν = m pm+2 [1]. 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...

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 =...

We analyze the modular properties of the effective CFT description for paired states, proposed in G. Cristofano, G. Maiella, V. Marrota, Mod. Phys. Lett. A 15 (2000) 1679, corresponding to the non-standard filling . We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of...

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 natur...

Crystal tensor operators, which transform under Uq→0(sl(2)), in analogous way as the vectors of the crystal basis, are introduced. The Wigner–Eckart theorem for the crystal tensor is defined: the selection rules depend on the initial state and on the component of the tensor operator; the transition amplitudes to the states of the same final irreduc...

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...

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...

From the extension of the covariant vertex operator construction for the affine Kac-Moody algebras to Lorentzian algebras, it is shown that the parafermionics realization of arbitrary level affine algebras can be interpreted in terms of bosonic realization. This connection is explicitly illustrated for level k=2 SU(2) algebra.

Crystal tensor operators, which tranform under U_q->0(sl(2)), in analogous way as the vectors of the crystal basis, are introduced. The Wigner-Eckart theorem for the crystal tensor is defined: the selection rules depend on the initial state and on the component of the tensor operator; the transition amplitudes to the states of the same final irredu...

We consider a class of conformal field theories on Riemann surfaces represented as a Zk invariant covering of the sphere. The introduction of exchange interactions among couples of sheets generate effective parafermions. The outgoing theory can be seen as a fractional supersymmetry conformal field theory.

The Wk structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to Wk algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of t...

We discuss a realization of stress-tensor for parafermion theories following a construction for higher level affine algebras, based on the projection of the standard level-one bosonic realization on the winding subalgebra. All the fields are obtained from rank free bosons compactified on torus, d. This gives an alternative realization of Virasoro a...

W_k structure underlying the tensverse realization of SU(2) at level k is analyzed. Extension of the equivalence existing between covariant and light-cone gauge realization of affine Kac-Moody algebra to W_k algebras is given. Higher spin generators related to parafermions are extracted from the operator product algebra of the generators and are sh...

The correlation function of the product of N generalized vertex operators satisfies an infinite set of Ward identities, related to a W_{\infty} algebra, whose extention out of the mass shell gives rise to equations which can be considered as a generalization of the compactified Calogero-Sutherland (CS) hamiltonians. In particular the wave function...

A vertex operator realization of generalized Kac-Moody algebras introduced by Borcherds is presented in the case of a single imaginary simple root. The structure of the fundamental representations is discussed. The possible relevance of the Borcherds algebra in many-particle field theory and in string theory is briefly discussed.

The main properties of indefinite Kac-Moody and Borcherds algebras, considered in a unified way as Lorentzian algebras, are reviewed. The connection with the conformal field theory of the vertex operator construction is discussed. By the folding procedure a class of subalgebras is obtained. Comment: 37 pages and 4 figures (not enclosed), Latex, DSF...

The main features of a hyperbolic Kac-Moody algebra (denoted by A1(1)), which appears in the dimensional reduction of N=1 supergravity from four to one dimensions, are presented. A vertex construction is exhibited and the structure of the fundamental representations is discussed. The vertex operator realization is presented in full generality, i.e....