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Sep 19, 2013
09/13

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Gerardo Cristofano; Giuseppe Maiella; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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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), which by construction reproduce the Quantum Hall topological properties at those fillings. Indeed for the Jain plateaux we find that the different...

Source: http://arxiv.org/abs/hep-th/0507111v1

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Sep 19, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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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.

Source: http://arxiv.org/abs/hep-th/0507110v3

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Sep 23, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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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. Cristofano et al., Eur. Phys. J. B 49 (2006) 83). That led us to predict the emergence of a topological order in such a system (G. Cristofano et al., JSTAT...

Source: http://arxiv.org/abs/0810.2920v1

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Sep 22, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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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 describe the model with different boundary conditions is shown. Special emphasis is given to the Mobius boundary conditions which generate a topological...

Source: http://arxiv.org/abs/0811.3688v1

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Sep 18, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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Following a suggestion given in Phys. Lett. B 571(2003) 621, we show how a bilayer Quantum Hall system at fillings nu =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 recent experimental findings (Phys. Rev. B 72 (2005) 041305) which evidence the presence of a topological defect in the transport...

Source: http://arxiv.org/abs/hep-th/0606252v1

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Sep 19, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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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.

Source: http://arxiv.org/abs/hep-th/0507238v1

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Sep 17, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Adele Naddeo; Giuliano Niccoli

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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 fractionalization (Eur. Phys. J. B 49 (2006) 83). The relevance of a ``closed'' geometry has been fully exploited in relating the topological properties of...

Source: http://arxiv.org/abs/0711.4245v1

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49

Jul 20, 2013
07/13

by
Gerardo Cristofano; Vincenzo Marotta; Giuliano Niccoli

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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 the RCFT U(1)xSU(m)$ proposed for the Jain states. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT...

Source: http://arxiv.org/abs/hep-th/0406076v1

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Sep 24, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Giuliano Niccoli

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We found new identities among the Dedekind eta-function, the characters of the W_{m} algebra and those of the level 1 affine Lie algebra su(m)_{1}. They allow to characterize the Z_{m}-orbifold of the m-component free bosons u(1)_{K_{m,p}} (our theory TM) as an extension of the fully degenerate representations of W_{1+infty}^{(m)}. In particular, TM is proven to be a Gamma _{theta}-RCFT extension of the chiral fully degenerate W_{1+infty}^{(m)}.

Source: http://arxiv.org/abs/hep-th/0412085v3

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Sep 18, 2013
09/13

by
Gerardo Cristofano; Vincenzo Marotta; Petter Minnhagen; Adele Naddeo; Giuliano Niccoli

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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;Nucl. Phys. B 641 (2002)547). The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the...

Source: http://arxiv.org/abs/hep-th/0606170v2

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Sep 21, 2013
09/13

by
Gesualdo Delfino; Giuliano Niccoli

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Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model.

Source: http://arxiv.org/abs/hep-th/0407142v2

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Sep 22, 2013
09/13

by
Gesualdo Delfino; Giuliano Niccoli

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The form factors of the descendant operators in the massive Lee-Yang model are determined up to level 7. This is first done by exploiting the conserved quantities of the integrable theory to generate the solutions for the descendants starting from the lowest non-trivial solutions in each operator family. We then show that the operator space generated in this way, which is isomorphic to the conformal one, coincides, level by level, with that implied by the $S$-matrix through the form factor...

Source: http://arxiv.org/abs/hep-th/0501173v1

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Sep 21, 2013
09/13

by
Gesualdo Delfino; Giuliano Niccoli

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The composite operator T\bar{T}, obtained from the components of the energy-momentum tensor, enjoys a quite general characterization in two-dimensional quantum field theory also away from criticality. We use the form factor bootstrap supplemented by asymptotic conditions to determine its matrix elements in the sinh-Gordon model. The results extend to the breather sector of the sine-Gordon model and to the minimal models M_{2/(2N+3)} perturbed by the operator phi_{1,3}.

Source: http://arxiv.org/abs/hep-th/0602223v1